Giugiuc, Leonard M.; Suceavă, Bogdan D. A class of strictly convex hypersurfaces satisfying Weingarten-type inequalities. I. (English) Zbl 07315981 Van der Veken, Joeri (ed.) et al., Geometry of submanifolds. AMS special session in honor of Bang-Yen Chen’s 75th birthday, University of Michigan, Ann Arbor, Michigan, October 20–21, 2018. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-5092-2/pbk; 978-1-4704-5666-5/ebook). Contemporary Mathematics 756, 121-131 (2020). MSC: 53B20 53B25 26D15 51M16 53A07 53A55 53C20 53C21 PDF BibTeX XML Cite \textit{L. M. Giugiuc} and \textit{B. D. Suceavă}, Contemp. Math. 756, 121--131 (2020; Zbl 07315981) Full Text: DOI
Chen, Bang-Yen \(g\)-Steiner, co-Steiner and normal points of bounded Euclidean submanifolds. (English) Zbl 07304398 Int. Electron. J. Geom. 13, No. 2, 1-10 (2020). MSC: 51M 52A20 53C40 52A39 PDF BibTeX XML Cite \textit{B.-Y. Chen}, Int. Electron. J. Geom. 13, No. 2, 1--10 (2020; Zbl 07304398) Full Text: DOI
Urbano, Francisco On hypersurfaces of \(\mathbb{S}^2 \times \mathbb{S}^2\). (English) Zbl 1429.53078 Commun. Anal. Geom. 27, No. 6, 1381-1416 (2019). MSC: 53C42 PDF BibTeX XML Cite \textit{F. Urbano}, Commun. Anal. Geom. 27, No. 6, 1381--1416 (2019; Zbl 1429.53078) Full Text: DOI arXiv
Giugiuc, Leonard M.; Suceava, Bogdan D. A characterization of cylinders and an estimate for mean curvature of convex Euclidean hypersurfaces satisfying a cylindrical condition. (English) Zbl 1419.53006 Int. Electron. J. Geom. 12, No. 1, 57-60 (2019). MSC: 53A07 PDF BibTeX XML Cite \textit{L. M. Giugiuc} and \textit{B. D. Suceava}, Int. Electron. J. Geom. 12, No. 1, 57--60 (2019; Zbl 1419.53006) Full Text: Link
Alodan, Haila; Chen, Bang-Yen; Deshmukh, Sharief; Vîlcu, Gabriel-Eduard On some geometric properties of quasi-product production models. (English) Zbl 07056516 J. Math. Anal. Appl. 474, No. 1, 693-711 (2019). MSC: 53A07 91B38 PDF BibTeX XML Cite \textit{H. Alodan} et al., J. Math. Anal. Appl. 474, No. 1, 693--711 (2019; Zbl 07056516) Full Text: DOI
Alías, Luis J.; Meléndez, Josué Remarks on hypersurfaces with constant higher order mean curvature in Euclidean space. (English) Zbl 1430.53060 Geom. Dedicata 199, 273-280 (2019). Reviewer: Yun Myung Oh (Berrien Springs) MSC: 53C40 53C42 PDF BibTeX XML Cite \textit{L. J. Alías} and \textit{J. Meléndez}, Geom. Dedicata 199, 273--280 (2019; Zbl 1430.53060) Full Text: DOI
Lima, Barnabé P.; Santos, Newton L.; Sousa, Paulo A. Generalized translation hypersurfaces in Euclidean space. (English) Zbl 1403.53009 J. Math. Anal. Appl. 470, No. 2, 1129-1135 (2019). MSC: 53A07 53C42 PDF BibTeX XML Cite \textit{B. P. Lima} et al., J. Math. Anal. Appl. 470, No. 2, 1129--1135 (2019; Zbl 1403.53009) Full Text: DOI
Diniz, M. M.; Vilhena, J. A. M.; Zapata, J. F. Z. Minimal hypersurfaces in \( {\mathbb{S}}^5\) with vanishing Gauss-Kronecker curvature. (English. Russian original) Zbl 1394.53063 Izv. Math. 82, No. 3, 477-493 (2018); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 82, No. 3, 31-48 (2018). MSC: 53C42 PDF BibTeX XML Cite \textit{M. M. Diniz} et al., Izv. Math. 82, No. 3, 477--493 (2018; Zbl 1394.53063); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 82, No. 3, 31--48 (2018) Full Text: DOI arXiv
Yang, Dan Some classifications of Weingarten translation hypersurfaces in Euclidean space. (English) Zbl 1399.53125 Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 61(109), No. 1, 107-115 (2018). MSC: 53D12 53C40 PDF BibTeX XML Cite \textit{D. Yang}, Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 61(109), No. 1, 107--115 (2018; Zbl 1399.53125)
de Almeida, S. C.; Brito, F. G. B.; Scherfner, M.; Weiss, S. On CMC hypersurfaces in \(\mathbb{S}^{n+1}\) with constant Gauß-Kronecker curvature. (English) Zbl 1391.53072 Adv. Geom. 18, No. 2, 187-192 (2018). MSC: 53C42 53C40 PDF BibTeX XML Cite \textit{S. C. de Almeida} et al., Adv. Geom. 18, No. 2, 187--192 (2018; Zbl 1391.53072) Full Text: DOI
Vîlcu, Alina-Daniela; Vîlcu, Gabriel-Eduard A survey on the geometry of production models in economics. (English) Zbl 1364.91079 Arab J. Math. Sci. 23, No. 1, 18-31 (2017). Reviewer: Aleksandr D. Borisenko (Kyïv) MSC: 91B38 53A07 91B02 PDF BibTeX XML Cite \textit{A.-D. Vîlcu} and \textit{G.-E. Vîlcu}, Arab J. Math. Sci. 23, No. 1, 18--31 (2017; Zbl 1364.91079) Full Text: DOI
Alencar, Hilário; do Carmo, Manfredo; Silva Neto, Gregório Stable hypersurfaces with zero scalar curvature in Euclidean space. (English) Zbl 1360.53016 Ark. Mat. 54, No. 2, 233-241 (2016). MSC: 53A07 53C42 PDF BibTeX XML Cite \textit{H. Alencar} et al., Ark. Mat. 54, No. 2, 233--241 (2016; Zbl 1360.53016) Full Text: DOI arXiv
Yang, Dan; Fu, Yu On affine translation surfaces in affine space. (English) Zbl 1339.53007 J. Math. Anal. Appl. 440, No. 2, 437-450 (2016). MSC: 53A15 PDF BibTeX XML Cite \textit{D. Yang} and \textit{Y. Fu}, J. Math. Anal. Appl. 440, No. 2, 437--450 (2016; Zbl 1339.53007) Full Text: DOI
Shu, S.; Chen, Junfeng Spacelike hypersurfaces with constant \(S\) or \(K\) in de Sitter Space or anti-de Sitter space. (English) Zbl 1373.53085 Bull. Iran. Math. Soc. 41, No. 4, 835-855 (2015). MSC: 53C42 53C50 PDF BibTeX XML Cite \textit{S. Shu} and \textit{J. Chen}, Bull. Iran. Math. Soc. 41, No. 4, 835--855 (2015; Zbl 1373.53085) Full Text: Link
Perdomo, Oscar M.; Wei, Guoxin A characterization of quadric constant Gauss-Kronecker curvature hypersurfaces of spheres. (English) Zbl 1322.53061 Asian J. Math. 19, No. 2, 251-264 (2015). Reviewer: Themistocles M. Rassias (Athens) MSC: 53C42 53A10 PDF BibTeX XML Cite \textit{O. M. Perdomo} and \textit{G. Wei}, Asian J. Math. 19, No. 2, 251--264 (2015; Zbl 1322.53061) Full Text: DOI
Kim, Dong-Soo Ellipsoids and elliptic hyperboloids in the Euclidean space \(\mathbb{E}^{n + 1}\). (English) Zbl 1312.53009 Linear Algebra Appl. 471, 28-45 (2015). MSC: 53A07 PDF BibTeX XML Cite \textit{D.-S. Kim}, Linear Algebra Appl. 471, 28--45 (2015; Zbl 1312.53009) Full Text: DOI
Wang, Xiaoshu A characterization of CES production functions having constant return to scale in microeconomics. (English) Zbl 1339.91072 Int. J. Appl. Math. Stat. 52, No. 2, 152-158 (2014). MSC: 91B38 35J96 53C42 PDF BibTeX XML Cite \textit{X. Wang}, Int. J. Appl. Math. Stat. 52, No. 2, 152--158 (2014; Zbl 1339.91072) Full Text: Link
Chen, Bang-Yen Solutions to homogeneous Monge-Ampère equations of homothetic functions and their applications to production models in economics. (English) Zbl 1442.35464 J. Math. Anal. Appl. 411, No. 1, 223-229 (2014). MSC: 35Q91 91B38 35J96 PDF BibTeX XML Cite \textit{B.-Y. Chen}, J. Math. Anal. Appl. 411, No. 1, 223--229 (2014; Zbl 1442.35464) Full Text: DOI arXiv
Suceava, Bogdan D. An estimate for the Gauss-Kronecker curvature of 3-dimensional smooth hypersurfaces in \(\mathbb E^4\). (English) Zbl 1303.53013 Int. Electron. J. Geom. 7, No. 2, 1-6 (2014). MSC: 53A07 PDF BibTeX XML Cite \textit{B. D. Suceava}, Int. Electron. J. Geom. 7, No. 2, 1--6 (2014; Zbl 1303.53013) Full Text: Link
Neto, G. Silva On stable hypersurfaces with vanishing scalar curvature. (English) Zbl 1297.53010 Math. Z. 277, No. 1-2, 481-497 (2014). Reviewer: Friedrich Manhart (Wien) MSC: 53A07 PDF BibTeX XML Cite \textit{G. S. Neto}, Math. Z. 277, No. 1--2, 481--497 (2014; Zbl 1297.53010) Full Text: DOI arXiv
Chen, Bang-Yen; Vîlcu, Gabriel Eduard Geometric classifications of homogeneous production functions. (English) Zbl 1334.91043 Appl. Math. Comput. 225, 345-351 (2013). MSC: 91B38 PDF BibTeX XML Cite \textit{B.-Y. Chen} and \textit{G. E. Vîlcu}, Appl. Math. Comput. 225, 345--351 (2013; Zbl 1334.91043) Full Text: DOI arXiv
Savas-Halilaj, Andreas On deformable minimal hypersurfaces in space forms. (English) Zbl 1273.53054 J. Geom. Anal. 23, No. 3, 1032-1057 (2013). MSC: 53C42 53B25 53A10 PDF BibTeX XML Cite \textit{A. Savas-Halilaj}, J. Geom. Anal. 23, No. 3, 1032--1057 (2013; Zbl 1273.53054) Full Text: DOI arXiv
Kim, Dong-Soo; Kim, Young Ho Some characterizations of spheres and elliptic paraboloids. II. (English) Zbl 1257.53012 Linear Algebra Appl. 438, No. 3, 1356-1364 (2013). MSC: 53A07 PDF BibTeX XML Cite \textit{D.-S. Kim} and \textit{Y. H. Kim}, Linear Algebra Appl. 438, No. 3, 1356--1364 (2013; Zbl 1257.53012) Full Text: DOI arXiv
Chen, Bang-Yen Classification of homothetic functions with constant elasticity of substitution and its geometric applications. (English) Zbl 1308.90060 Int. Electron. J. Geom. 5, No. 2, 67-78 (2012). MSC: 90B30 53C40 91B38 PDF BibTeX XML Cite \textit{B.-Y. Chen}, Int. Electron. J. Geom. 5, No. 2, 67--78 (2012; Zbl 1308.90060) Full Text: Link
Chen, Bang-Yen A note on homogeneous production models. (English) Zbl 1299.91088 Kragujevac J. Math. 36, No. 1, 41-43 (2012). MSC: 91B38 91B64 53B25 PDF BibTeX XML Cite \textit{B.-Y. Chen}, Kragujevac J. Math. 36, No. 1, 41--43 (2012; Zbl 1299.91088)
Chen, Bang-Yen Geometry of quasi-sum production functions with constant elasticity of substitution property. (English) Zbl 1273.90072 J. Adv. Math. Stud. 5, No. 2, 90-97 (2012). MSC: 90B30 91B38 PDF BibTeX XML Cite \textit{B.-Y. Chen}, J. Adv. Math. Stud. 5, No. 2, 90--97 (2012; Zbl 1273.90072)
Chaves, R. M. B.; Sousa, L. A. M. jun.; Valério, B. C. New characterizations for hyperbolic cylinders in anti-de Sitter spaces. (English) Zbl 1243.53016 J. Math. Anal. Appl. 393, No. 1, 166-176 (2012). MSC: 53B25 53B30 PDF BibTeX XML Cite \textit{R. M. B. Chaves} et al., J. Math. Anal. Appl. 393, No. 1, 166--176 (2012; Zbl 1243.53016) Full Text: DOI
Chen, Bang-Yen On some geometric properties of quasi-sum production models. (English) Zbl 1243.39019 J. Math. Anal. Appl. 392, No. 2, 192-199 (2012). MSC: 39B52 39B22 91B38 90B30 PDF BibTeX XML Cite \textit{B.-Y. Chen}, J. Math. Anal. Appl. 392, No. 2, 192--199 (2012; Zbl 1243.39019) Full Text: DOI
Chen, Bang-Yen On some geometric properties of \(h\)-homogeneous production functions in microeconomics. (English) Zbl 1289.91107 Kragujevac J. Math. 35, No. 3, 343-357 (2011). Reviewer: Miroslava Torgašev-Petrović (Kragujevac) MSC: 91B38 91B64 53B25 PDF BibTeX XML Cite \textit{B.-Y. Chen}, Kragujevac J. Math. 35, No. 3, 343--357 (2011; Zbl 1289.91107)
Wu, Yadong; Zhao, Guosong Hypersurfaces with Li-normalization and prescribed Gauss-Kronecker curvature. (English) Zbl 1232.53018 Result. Math. 59, No. 3-4, 563-576 (2011). Reviewer: Despina Papadopoulou-Florou (Thessaloniki) MSC: 53A15 35J60 35J65 53C20 53C21 53C42 PDF BibTeX XML Cite \textit{Y. Wu} and \textit{G. Zhao}, Result. Math. 59, No. 3--4, 563--576 (2011; Zbl 1232.53018) Full Text: DOI
Wu, Yadong Asymptotic behaviors of hyperbolic hypersurfaces with constant affine Gauss-Kronecker curvature. (English) Zbl 1220.53016 Result. Math. 59, No. 1-2, 173-183 (2011). Reviewer: Kurt Leichtweiß (Stuttgart) MSC: 53A15 PDF BibTeX XML Cite \textit{Y. Wu}, Result. Math. 59, No. 1--2, 173--183 (2011; Zbl 1220.53016) Full Text: DOI
Asperti, A. C.; Chaves, R. M. B.; Sousa, L. A. M. jun. The Gauss-Kronecker curvature of minimal hypersurfaces in four-dimensional space forms. (English) Zbl 1225.53057 Math. Z. 267, No. 3-4, 523-533 (2011). Reviewer: Alexander A. Borisenko (Khar’kov) MSC: 53C42 53B25 53C24 PDF BibTeX XML Cite \textit{A. C. Asperti} et al., Math. Z. 267, No. 3--4, 523--533 (2011; Zbl 1225.53057) Full Text: DOI
Grinberg, Eric L.; Li, Haizhong The Gauss-Bonnet-Grotemeyer theorem in space forms. (English) Zbl 1208.53059 Inverse Probl. Imaging 4, No. 4, 655-664 (2010). Reviewer: Constantin Călin (Iaşi) MSC: 53C40 53A10 PDF BibTeX XML Cite \textit{E. L. Grinberg} and \textit{H. Li}, Inverse Probl. Imaging 4, No. 4, 655--664 (2010; Zbl 1208.53059) Full Text: DOI Link
Fu, Yu; Hou, Zhong-Hua Affine translation surfaces with constant Gaussian curvature. (English) Zbl 1198.53006 Kyungpook Math. J. 50, No. 2, 337-343 (2010). MSC: 53A05 PDF BibTeX XML Cite \textit{Y. Fu} and \textit{Z.-H. Hou}, Kyungpook Math. J. 50, No. 2, 337--343 (2010; Zbl 1198.53006) Full Text: DOI Link
Cheng, Qing-Ming; Li, Haizhong; Wei, Guoxin On some rigidity results of hypersurfaces in a sphere. (English) Zbl 1206.53061 Proc. R. Soc. Edinb., Sect. A, Math. 140, No. 3, 477-493 (2010). Reviewer: Mukut Mani Tripathi (Varanasi) MSC: 53C40 53C24 PDF BibTeX XML Cite \textit{Q.-M. Cheng} et al., Proc. R. Soc. Edinb., Sect. A, Math. 140, No. 3, 477--493 (2010; Zbl 1206.53061) Full Text: DOI
Cheng, Fei; Zhou, Jiazu The nonconvex surface with positive mean curvature. (Chinese. English summary) Zbl 1212.53003 J. Math., Wuhan Univ. 29, No. 3, 359-362 (2009). MSC: 53A05 53C65 PDF BibTeX XML Cite \textit{F. Cheng} and \textit{J. Zhou}, J. Math., Wuhan Univ. 29, No. 3, 359--362 (2009; Zbl 1212.53003)
Xu, Hongwei; Zhao, Entao Complete hypersurfaces in a 4-dimensional hyperbolic space. (English) Zbl 1212.53064 Appl. Math., Ser. B (Engl. Ed.) 24, No. 3, 370-378 (2009). MSC: 53C24 53C40 53A10 PDF BibTeX XML Cite \textit{H. Xu} and \textit{E. Zhao}, Appl. Math., Ser. B (Engl. Ed.) 24, No. 3, 370--378 (2009; Zbl 1212.53064) Full Text: DOI
Huang, Yong; Jian, Huaiyu; Su, Ning Spacelike hypersurfaces of prescribed Gauss-Kronecker curvature in exterior domains. (English) Zbl 1187.53018 Acta Math. Sin., Engl. Ser. 25, No. 3, 491-502 (2009). MSC: 53B25 53B30 35J93 PDF BibTeX XML Cite \textit{Y. Huang} et al., Acta Math. Sin., Engl. Ser. 25, No. 3, 491--502 (2009; Zbl 1187.53018) Full Text: DOI
Wang, Bao Fu The affine complete hypersurfaces of constant Gauss-Kronecker curvature. (English) Zbl 1173.53008 Acta Math. Sin., Engl. Ser. 25, No. 8, 1353-1362 (2009). Reviewer: Udo Simon (Berlin) MSC: 53A15 35G30 58J32 58J60 PDF BibTeX XML Cite \textit{B. F. Wang}, Acta Math. Sin., Engl. Ser. 25, No. 8, 1353--1362 (2009; Zbl 1173.53008) Full Text: DOI
Dursun, U. On minimal hypersurfaces of hyperbolic space \(\mathbb H^4\) with zero Gauss-Kronecker curvature. (English) Zbl 1162.53317 Kowalski, Oldřich (ed.) et al., Differential geometry and its applications. Proceedings of the 10th international conference on differential geometry and its applications, DGA 2007, Olomouc, Czech Republic, August 27–31, 2007. Hackensack, NJ: World Scientific (ISBN 978-981-279-060-6/hbk). 77-87 (2008). MSC: 53C42 PDF BibTeX XML Cite \textit{U. Dursun}, in: Differential geometry and its applications. Proceedings of the 10th international conference on differential geometry and its applications, DGA 2007, Olomouc, Czech Republic, August 27--31, 2007. Hackensack, NJ: World Scientific. 77--87 (2008; Zbl 1162.53317) Full Text: DOI
Izumiya, Shyuichi; Romero Fuster, María del Carmen The total lightcone Gauss-Kronecker curvature on codimension two spacelike submanifolds in Lorentz space. (English) Zbl 1228.53023 Iglesias Ponte, David (ed.) et al., Proceedings of the XV international workshop on geometry and physics, Puerto de la Cruz, Spain, September 11–16, 2006. Madrid: Real Sociedad Matemática Española (ISBN 978-84-935196-1-2/pbk). Publicaciones de la Real Sociedad Matemática Española 11, 153-160 (2007). MSC: 53B25 58K05 53A35 PDF BibTeX XML Cite \textit{S. Izumiya} and \textit{M. d. C. Romero Fuster}, in: Proceedings of the XV international workshop on geometry and physics, Puerto de la Cruz, Spain, September 11--16, 2006. Madrid: Real Sociedad Matemática Española. 153--160 (2007; Zbl 1228.53023)
Wang, Baofu The affine complete hypersurfaces with prescribed affine curvature. (English) Zbl 1164.53309 J. Sichuan Univ., Nat. Sci. Ed. 44, No. 4, 729-732 (2007). MSC: 53A15 PDF BibTeX XML Cite \textit{B. Wang}, J. Sichuan Univ., Nat. Sci. Ed. 44, No. 4, 729--732 (2007; Zbl 1164.53309)
Izumiya, Shyuichi; Romero Fuster, María del Carmen The lightlike flat geometry on spacelike submanifolds of codimension two in Minkowski space. (English) Zbl 1141.53066 Sel. Math., New Ser. 13, No. 1, 23-55 (2007). Reviewer: Vasyl Gorkaviy (Kharkov) MSC: 53C50 53B25 53B30 58K05 PDF BibTeX XML Cite \textit{S. Izumiya} and \textit{M. d. C. Romero Fuster}, Sel. Math., New Ser. 13, No. 1, 23--55 (2007; Zbl 1141.53066) Full Text: DOI
Aledo, Juan A.; Espinar, José M. A conformal representation for linear Weingarten surfaces in the de Sitter space. (English) Zbl 1121.53040 J. Geom. Phys. 57, No. 8, 1669-1677 (2007). Reviewer: Serguey M. Pokas (Odessa) MSC: 53C42 53C50 PDF BibTeX XML Cite \textit{J. A. Aledo} and \textit{J. M. Espinar}, J. Geom. Phys. 57, No. 8, 1669--1677 (2007; Zbl 1121.53040) Full Text: DOI
Hasanis, Th.; Savas-Halilaj, A.; Vlachos, Th. Complete minimal hypersurfaces in \(\mathbb{S}^4\) with zero Gauss-Kronecker curvature. (English) Zbl 1114.53056 Math. Proc. Camb. Philos. Soc. 142, No. 1, 125-132 (2007). Reviewer: Ülo Lumiste (Tartu) MSC: 53C42 PDF BibTeX XML Cite \textit{Th. Hasanis} et al., Math. Proc. Camb. Philos. Soc. 142, No. 1, 125--132 (2007; Zbl 1114.53056) Full Text: DOI arXiv
Hasanis, T.; Savas-Halilaj, A.; Vlachos, T. Complete minimal hypersurfaces in the hyperbolic space \(\mathbb{H}^{4}\) with vanishing Gauss-Kronecker curvature. (English) Zbl 1113.53038 Trans. Am. Math. Soc. 359, No. 6, 2799-2818 (2007). Reviewer: Ülo Lumiste (Tartu) MSC: 53C40 PDF BibTeX XML Cite \textit{T. Hasanis} et al., Trans. Am. Math. Soc. 359, No. 6, 2799--2818 (2007; Zbl 1113.53038) Full Text: DOI arXiv
Mikula, Richard Prescribing Gauss-Kronecker curvature on group invariant convex hypersurfaces. (English) Zbl 1212.53083 Differ. Integral Equ. 19, No. 10, 1103-1128 (2006). MSC: 53C42 58J05 32F99 PDF BibTeX XML Cite \textit{R. Mikula}, Differ. Integral Equ. 19, No. 10, 1103--1128 (2006; Zbl 1212.53083)
Alías, Luis J.; Kurose, Takashi; Solanes, Gil Hadamard-type theorems for hypersurfaces in hyperbolic spaces. (English) Zbl 1103.52006 Differ. Geom. Appl. 24, No. 5, 492-502 (2006). MSC: 52A55 53C40 PDF BibTeX XML Cite \textit{L. J. Alías} et al., Differ. Geom. Appl. 24, No. 5, 492--502 (2006; Zbl 1103.52006) Full Text: DOI
Cheng, Qing-Ming; Suh, Young Jin Maximal space-like hypersurfaces in \(H_{1}^{4}(-1)\) with zero Gauss-Kronecker curvature. (English) Zbl 1092.53047 J. Korean Math. Soc. 43, No. 1, 147-157 (2006). Reviewer: Andreas Gastel (Düsseldorf) MSC: 53C42 53C20 PDF BibTeX XML Cite \textit{Q.-M. Cheng} and \textit{Y. J. Suh}, J. Korean Math. Soc. 43, No. 1, 147--157 (2006; Zbl 1092.53047) Full Text: DOI
Andrica, Dorin; Pintea, Cornel Mappings with uncountably many topological critical points and applications to some curvature problems. (English) Zbl 1144.57304 Nonlinear Funct. Anal. Appl. 10, No. 5, 691-700 (2005). MSC: 57R70 55M30 PDF BibTeX XML Cite \textit{D. Andrica} and \textit{C. Pintea}, Nonlinear Funct. Anal. Appl. 10, No. 5, 691--700 (2005; Zbl 1144.57304)
Hasanis, T.; Savas-Halilaj, A.; Vlachos, T. Minimal hypersurfaces with zero Gauss-Kronecker curvature. (English) Zbl 1087.53056 Ill. J. Math. 49, No. 2, 523-529 (2005). Reviewer: Wayne Rossman (Kobe) MSC: 53C42 53A10 PDF BibTeX XML Cite \textit{T. Hasanis} et al., Ill. J. Math. 49, No. 2, 523--529 (2005; Zbl 1087.53056) Full Text: Link arXiv
Lusala, Tsasa; Gomes de Oliveira, André Closed hypersurfaces of \(\mathbb S^4(1)\) with constant mean curvature and zero Gauß-Kronecker curvature. (English) Zbl 1069.53049 C. R., Math., Acad. Sci. Paris 340, No. 6, 437-440 (2005). MSC: 53C42 PDF BibTeX XML Cite \textit{T. Lusala} and \textit{A. Gomes de Oliveira}, C. R., Math., Acad. Sci. Paris 340, No. 6, 437--440 (2005; Zbl 1069.53049) Full Text: DOI
Cheng, Qing-Ming Curvatures of complete hypersurfaces in space forms. (English) Zbl 1074.53044 Proc. R. Soc. Edinb., Sect. A, Math. 134, No. 1, 55-68 (2004). Reviewer: Vicente Cortés (Vandœuvre-lés-Nancy) MSC: 53C40 PDF BibTeX XML Cite \textit{Q.-M. Cheng}, Proc. R. Soc. Edinb., Sect. A, Math. 134, No. 1, 55--68 (2004; Zbl 1074.53044) Full Text: DOI
Lusala, Tsasa Non-closed minimal hypersurfaces of \(\mathbb{S}^4(1)\) with identically zero Gauß-Kronecker curvature. (English) Zbl 1051.53014 Hokkaido Math. J. 33, No. 1, 65-82 (2004). Reviewer: Li Haizhong (Beijing) MSC: 53B25 53C40 53C42 PDF BibTeX XML Cite \textit{T. Lusala}, Hokkaido Math. J. 33, No. 1, 65--82 (2004; Zbl 1051.53014) Full Text: DOI arXiv
Cao, Jianguo; Escobar, José F. A new 3-dimensional curvature integral formula for PL-manifolds of non-positive curvature. (English) Zbl 1101.57009 Commun. Anal. Geom. 11, No. 3, 489-551 (2003). Reviewer: Maria Rita Casali (Modena) MSC: 57N16 57M50 57Q99 PDF BibTeX XML Cite \textit{J. Cao} and \textit{J. F. Escobar}, Commun. Anal. Geom. 11, No. 3, 489--551 (2003; Zbl 1101.57009) Full Text: DOI
Cheng, Li-Tien Construction of shapes arising from the Minkowski problem using a level set approach. (English) Zbl 1035.65093 J. Sci. Comput. 19, No. 1-3, 123-138 (2003). MSC: 65M06 35L70 PDF BibTeX XML Cite \textit{L.-T. Cheng}, J. Sci. Comput. 19, No. 1--3, 123--138 (2003; Zbl 1035.65093) Full Text: DOI
Křížek, Michal; Pradlová, Jana On the nonexistence of a Lobachevsky geometry model of an isotropic and homogeneous universe. (English) Zbl 1011.83046 Math. Comput. Simul. 61, No. 3-6, 525-535 (2003). MSC: 83F05 53C80 PDF BibTeX XML Cite \textit{M. Křížek} and \textit{J. Pradlová}, Math. Comput. Simul. 61, No. 3--6, 525--535 (2003; Zbl 1011.83046) Full Text: DOI
Efremov, R. V.; Kamenev, G. K. A priori estimate for asymptotic efficiency of one class of algorithms for polyhedral approximation of convex bodies. (Russian, English) Zbl 1057.52001 Zh. Vychisl. Mat. Mat. Fiz. 42, No. 1, 23-32 (2002); translation in Comput. Math. Math. Phys. 42, No. 1, 20-29 (2002). Reviewer: Andrei Zemskov (Moskva) MSC: 52A27 52B55 PDF BibTeX XML Cite \textit{R. V. Efremov} and \textit{G. K. Kamenev}, Zh. Vychisl. Mat. Mat. Fiz. 42, No. 1, 23--32 (2002; Zbl 1057.52001); translation in Comput. Math. Math. Phys. 42, No. 1, 20--29 (2002)
Cheng, Yongjun; Chen, Qing Several spherial theorems on immersed hypersurface in Euclidean space. (Chinese. English summary) Zbl 1054.53007 J. Univ. Sci. Technol. China 32, No. 6, 643-648 (2002). Reviewer: Li Haizhong (Beijing) MSC: 53A07 53C42 53C40 PDF BibTeX XML Cite \textit{Y. Cheng} and \textit{Q. Chen}, J. Univ. Sci. Technol. China 32, No. 6, 643--648 (2002; Zbl 1054.53007)
Guo, Zhen; Chen, Weihuan; Chen, Jianhua On affine deformation preserving the Gauss map. (Chinese. English summary) Zbl 1029.53065 Acta Math. Sin. 45, No. 1, 157-164 (2002). Reviewer: Mingliang Cai (Coral Gables) MSC: 53C40 53A15 PDF BibTeX XML Cite \textit{Z. Guo} et al., Acta Math. Sin. 45, No. 1, 157--164 (2002; Zbl 1029.53065)
Ghomi, Mohammad Gauss map, topology, and convexity of hypersurfaces with nonvanishing curvature. (English) Zbl 0993.57009 Topology 41, No. 1, 107-117 (2002). Reviewer: Sebastian Goette (Tübingen) MSC: 57N35 53A05 53A10 PDF BibTeX XML Cite \textit{M. Ghomi}, Topology 41, No. 1, 107--117 (2002; Zbl 0993.57009) Full Text: DOI
Borbély, Albert On the total curvature of convex hypersurfaces in hyperbolic spaces. (English) Zbl 1058.53049 Proc. Am. Math. Soc. 130, No. 3, 849-854 (2002). MSC: 53C42 53C21 PDF BibTeX XML Cite \textit{A. Borbély}, Proc. Am. Math. Soc. 130, No. 3, 849--854 (2002; Zbl 1058.53049) Full Text: DOI
Liao, Hua-kui Surfaces with affine Gauss-Kronecker curvature zero. (English) Zbl 0997.53009 Arch. Math. 76, No. 2, 149-160 (2001). Reviewer: L.Vanhecke (Leuven) MSC: 53A15 PDF BibTeX XML Cite \textit{H.-k. Liao}, Arch. Math. 76, No. 2, 149--160 (2001; Zbl 0997.53009) Full Text: DOI
Berestovskij, V. N.; Zubareva, I. A. On regularity and the Gauss-Kronecker curvatures of the boundaries of dual bodies. (Russian. English summary) Zbl 0987.53028 Vodop’yanov, S. K. (ed.), Proceedings on analysis and geometry. International conference in honor of the 70th birthday of Professor Yu. G. Reshetnyak, Novosibirsk, Russia, August 30-September 3, 1999. Novosibirsk: Izdatel’stvo Instituta Matematiki Im. S. L. Soboleva SO RAN. 73-81 (2000). Reviewer: I.A.Taimanov (Novosibirsk) MSC: 53C45 30C70 30C75 30C65 PDF BibTeX XML Cite \textit{V. N. Berestovskij} and \textit{I. A. Zubareva}, in: Trudy po analizu i geometrii. Novosibirsk: Izdatel'stvo Instituta Matematiki Im. S. L. Soboleva SO RAN. 73--81 (2000; Zbl 0987.53028)
Li, An-Min; Jia, Fang Affine differential geometry and partial differential equations of fourth order. (English) Zbl 1009.53012 Chen, W. H. (ed.) et al., Geometry and topology of submanifolds X. Proceedings of the conference on differential geometry in honor of Prof. S. S. Chern, Beijing, China, August 29-September 3, 1999 and the workshop on PDEs and submanifolds, Berlin, Germany, November 26-28, 1999. Singapore: World Scientific. 136-144 (2000). Reviewer: F.Manhart (Wien) MSC: 53A15 53C40 58J05 58J60 35G25 PDF BibTeX XML Cite \textit{A.-M. Li} and \textit{F. Jia}, in: Geometry and topology of submanifolds X. Proceedings of the conference on differential geometry in honor of Prof. S. S. Chern, Beijing, China, August 29--September 3, 1999 and the workshop on PDEs and submanifolds, Berlin, Germany, November 26--28, 1999. Singapore: World Scientific. 136--144 (2000; Zbl 1009.53012)
Chai, Y. D.; Kim, Moonjeong On a generalization of Fenchel’s theorem. (English) Zbl 1024.53003 Commun. Korean Math. Soc. 15, No. 1, 103-109 (2000). MSC: 53A04 52A10 PDF BibTeX XML Cite \textit{Y. D. Chai} and \textit{M. Kim}, Commun. Korean Math. Soc. 15, No. 1, 103--109 (2000; Zbl 1024.53003)
Li, Anmin; Simon, Udo; Zhao, Guosong Hypersurfaces with prescribed affine Gauss-Kronecker curvature. (English) Zbl 0972.53013 Geom. Dedicata 81, No. 1-3, 141-166 (2000). Reviewer: Luc Vrancken (Utrecht) MSC: 53A15 PDF BibTeX XML Cite \textit{A. Li} et al., Geom. Dedicata 81, No. 1--3, 141--166 (2000; Zbl 0972.53013) Full Text: DOI
Defever, Filip Conformally flat hypersurfaces with constant Gauss-Kronecker curvature. (English) Zbl 0978.53009 Bull. Aust. Math. Soc. 61, No. 2, 207-216 (2000). Reviewer: Oscar J.Garay (Bilbao) MSC: 53A07 53B20 PDF BibTeX XML Cite \textit{F. Defever}, Bull. Aust. Math. Soc. 61, No. 2, 207--216 (2000; Zbl 0978.53009) Full Text: DOI
Xu, Zhicai On spacelike hypersurfaces with constant mean curvature in de Sitter space. (Chinese. English summary) Zbl 1015.53038 Acta Math. Sin. 42, No. 5, 787-794 (1999). MSC: 53C42 53C50 PDF BibTeX XML Cite \textit{Z. Xu}, Acta Math. Sin. 42, No. 5, 787--794 (1999; Zbl 1015.53038)
Manhart, F. On affine curvature theory of Euclidean minimal surfaces. (Zur affinen Krümmungstheorie euklidischer Minimalflächen.) (German) Zbl 0968.53012 Röschel, O. (ed.) et al., Geometrie-Tagung “107 Jahre Drehfluchtprinzip”, Vorau, Österreich, 1. Juni-6. Juni 1997. Tagungsband. Vorau: TU Graz, 121-130 (1999). Reviewer: Udo Simon (Berlin) MSC: 53A15 53A10 PDF BibTeX XML Cite \textit{F. Manhart}, in: Geometrie-Tagung ``107 Jahre Drehfluchtprinzip'', Vorau, Österreich, 1. Juni--6. Juni 1997. Tagungsband. Vorau: TU Graz. 121--130 (1999; Zbl 0968.53012)
Brasil, Aldir jun. Hypersurfaces with constant mean curvature and constant quasi-Gauss-Kronecker curvature in \(S^4\). (English) Zbl 0954.53034 An. Acad. Bras. Ciênc. 71, No. 4, Pt. I, 599-605 (1999). Reviewer: V.Cruceanu (Iaşi) MSC: 53C40 PDF BibTeX XML Cite \textit{A. Brasil jun.}, An. Acad. Bras. Ciênc. 71, No. 4, Part I, 599--605 (1999; Zbl 0954.53034)
Lee, Seung-Won; Koh, Sung-Eun Another characterization of round spheres. (English) Zbl 0951.53038 Bull. Korean Math. Soc. 36, No. 4, 701-706 (1999). Reviewer: C.S.Houh (Detroit) MSC: 53C40 53C42 PDF BibTeX XML Cite \textit{S.-W. Lee} and \textit{S.-E. Koh}, Bull. Korean Math. Soc. 36, No. 4, 701--706 (1999; Zbl 0951.53038)
Alencar, Hilário; do Carmo, Manfredo; Elbert, Maria Fernanda Stable minimal hypersurfaces in Euclidean spaces. (English) Zbl 0949.53044 An. Acad. Bras. Ciênc. 70, No. 3, 387-391 (1998). Reviewer: Ch.Baikoussis (Ioannina) MSC: 53C42 53A10 53A07 PDF BibTeX XML Cite \textit{H. Alencar} et al., An. Acad. Bras. Ciênc. 70, No. 3, 387--391 (1998; Zbl 0949.53044)
Heil, Erhard Rotational hypersurfaces of constant Gauss-Kronecker curvature. (English) Zbl 0943.53007 J. Natl. Acad. Math. India 11(1997), 39-47 (1999). Reviewer: Rolf Walter (Dortmund) MSC: 53A07 PDF BibTeX XML Cite \textit{E. Heil}, J. Natl. Acad. Math. India 11, 39--47 (1997; Zbl 0943.53007)
Sheng, Weimin On Harnack’s inequality for some Gauss-Kronecker curvature flow. (Chinese. English summary) Zbl 0911.53024 J. Hangzhou Univ., Nat. Sci. Ed. 24, No. 3, 195-203 (1997). Reviewer: Zhu Fulin (Hubei) MSC: 53C21 35G10 35K25 PDF BibTeX XML Cite \textit{W. Sheng}, J. Hangzhou Univ., Nat. Sci. Ed. 24, No. 3, 195--203 (1997; Zbl 0911.53024)
Nelli, Barbara; Rosenberg, Harold Some remarks on positive scalar and Gauss-Kronecker curvature hypersurfaces of \({\mathbb R}^{n+1}\) and \({\mathbb H}^{n+1}\). (English) Zbl 0878.53007 Ann. Inst. Fourier 47, No. 4, 1209-1218 (1997). MSC: 53A07 PDF BibTeX XML Cite \textit{B. Nelli} and \textit{H. Rosenberg}, Ann. Inst. Fourier 47, No. 4, 1209--1218 (1997; Zbl 0878.53007) Full Text: DOI Numdam EuDML
Li, Yan Yan Group invariant convex hypersurfaces with prescribed Gauss-Kronecker curvature. (English) Zbl 0881.53051 Cordaro, Paulo D. (ed.) et al., Multidimensional complex analysis and partial differential equations. A collection of papers in honor of François Treves. Proceedings of the Brazil-USA conference, June 12–16, 1995, São Carlos, Brazil. Providence, RI: American Mathematical Society. Contemp. Math. 205, 203-218 (1997). Reviewer: T.Hasanis (Ioannina) MSC: 53C42 58J05 53C40 PDF BibTeX XML Cite \textit{Y. Y. Li}, Contemp. Math. 205, 203--218 (1997; Zbl 0881.53051)
Shen, Yibing; Sheng, Weimin Deforming convex hypersurfaces by the linear combination of the mean curvature and the \(n\)-th root of the Gauss-Kronecker curvature. (English) Zbl 0879.53008 Acta Math. Sci. (Engl. Ed.) 17, No. 2, 129-142 (1997). Reviewer: J.Urbas (Bonn) MSC: 53A07 35G10 35K25 PDF BibTeX XML Cite \textit{Y. Shen} and \textit{W. Sheng}, Acta Math. Sci. (Engl. Ed.) 17, No. 2, 129--142 (1997; Zbl 0879.53008)
Carneiro de Almeida, Sebastião; Braga Brito, Fabiano Gustavo Closed hypersurfaces of \(S^ 4\) with constant Gauss-Kronecker curvature. (English) Zbl 0864.53042 Mat. Contemp. 9, 15-22 (1995). Reviewer: L.K.H.Kramer (Würzburg) MSC: 53C42 PDF BibTeX XML Cite \textit{S. Carneiro de Almeida} and \textit{F. G. Braga Brito}, Mat. Contemp. 9, 15--22 (1995; Zbl 0864.53042)
Schütt, Carsten Random polytopes and affine surface area. (English) Zbl 0818.52004 Math. Nachr. 170, 227-249 (1994). Reviewer: I.S.Molchanov (Amsterdam) MSC: 52A22 PDF BibTeX XML Cite \textit{C. Schütt}, Math. Nachr. 170, 227--249 (1994; Zbl 0818.52004) Full Text: DOI
Kojima, Masatoshi \(q\)-conformally flat manifolds. (English) Zbl 0824.53013 Kyushu J. Math. 48, No. 2, 357-378 (1994). Reviewer: Z.Jankovsky (Praha) MSC: 53A30 PDF BibTeX XML Cite \textit{M. Kojima}, Kyushu J. Math. 48, No. 2, 357--378 (1994; Zbl 0824.53013) Full Text: DOI
Rosenberg, Harold; Spruck, Joel On the existence of convex hypersurfaces of constant Gauss curvature in hyperbolic space. (English) Zbl 0823.53047 J. Differ. Geom. 40, No. 2, 379-409 (1994). Reviewer: M.Craioveanu (Timişoara) MSC: 53C42 PDF BibTeX XML Cite \textit{H. Rosenberg} and \textit{J. Spruck}, J. Differ. Geom. 40, No. 2, 379--409 (1994; Zbl 0823.53047) Full Text: DOI
Cheng, Qing-Ming Hypersurfaces of a Lorentz space form. (English) Zbl 0806.53057 Arch. Math. 63, No. 3, 271-281 (1994). Reviewer: Qing-Ming Cheng (Trieste) MSC: 53C40 53C50 PDF BibTeX XML Cite \textit{Q.-M. Cheng}, Arch. Math. 63, No. 3, 271--281 (1994; Zbl 0806.53057) Full Text: DOI
Cheng, Qing-Ming Complete maximal spacelike hypersurfaces of \(H_ 1^ 4(c)\). (English) Zbl 0804.53088 Manuscr. Math. 82, No. 2, 149-160 (1994). Reviewer: B.Rouxel (Quimper) MSC: 53C42 53C50 PDF BibTeX XML Cite \textit{Q.-M. Cheng}, Manuscr. Math. 82, No. 2, 149--160 (1994; Zbl 0804.53088) Full Text: DOI EuDML
Schütt, Carsten On the affine surface area. (English) Zbl 0784.52004 Proc. Am. Math. Soc. 118, No. 4, 1213-1218 (1993). Reviewer: L.A.Santaló (Buenos Aires) MSC: 52A20 53A15 52A38 PDF BibTeX XML Cite \textit{C. Schütt}, Proc. Am. Math. Soc. 118, No. 4, 1213--1218 (1993; Zbl 0784.52004) Full Text: DOI
Cheng, Qingming Hypersurfaces with constant quasi-Gauss-Kronecker curvature in \(S^ 4(1)\). (English) Zbl 0790.53004 Adv. Math., Beijing 22, No. 2, 125-132 (1993). Reviewer: St.Hineva (Sofia) MSC: 53A07 53B25 PDF BibTeX XML Cite \textit{Q. Cheng}, Adv. Math., Beijing 22, No. 2, 125--132 (1993; Zbl 0790.53004)
Tso, Kaising A direct method approach for the existence of convex hypersurfaces with prescribed Gauss-Kronecker curvature. (English) Zbl 0735.53048 Math. Z. 209, No. 3, 339-344 (1992). Reviewer: K.Tso (Hong Kong) MSC: 53C45 53C42 35J60 PDF BibTeX XML Cite \textit{K. Tso}, Math. Z. 209, No. 3, 339--344 (1992; Zbl 0735.53048) Full Text: DOI EuDML
Tso, Kaising Convex hypersurfaces with prescribed Gauss-Kronecker curvature. (English) Zbl 0723.53041 J. Differ. Geom. 34, No. 2, 389-410 (1991). Reviewer: Tso Kaising (Hongkong) MSC: 53C45 53A05 35J50 PDF BibTeX XML Cite \textit{K. Tso}, J. Differ. Geom. 34, No. 2, 389--410 (1991; Zbl 0723.53041) Full Text: DOI
Martínez, A.; Milán, F. Convex affine surfaces with constant affine mean curvature. (English) Zbl 0749.53005 Global differential geometry and global analysis, Proc. Conf., Berlin/Ger. 1990, Lect. Notes Math. 1481, 138-144 (1991). Reviewer: Li Anmin (Chengdu) MSC: 53A15 53C45 PDF BibTeX XML
Ramanathan, Jayakumar Minimal hypersurfaces in \(S^ 4\) with vanishing Gauss-Kronecker curvature. (English) Zbl 0694.53054 Math. Z. 205, No. 4, 645-658 (1990). Reviewer: J.Ramanathan MSC: 53C42 PDF BibTeX XML Cite \textit{J. Ramanathan}, Math. Z. 205, No. 4, 645--658 (1990; Zbl 0694.53054) Full Text: DOI EuDML
Almeida, Sebastião C.; Brito, Fabiano Minimal hypersurfaces of \(S^ 4\) with constant Gauss-Kronecker curvature. (English) Zbl 0602.53040 Math. Z. 195, 99-107 (1987). MSC: 53C42 PDF BibTeX XML Cite \textit{S. C. Almeida} and \textit{F. Brito}, Math. Z. 195, 99--107 (1987; Zbl 0602.53040) Full Text: DOI EuDML
Tso, Kaising Deforming a hypersurface by its Gauss-Kronecker curvature. (English) Zbl 0612.53005 Commun. Pure Appl. Math. 38, 867-882 (1985). Reviewer: R.Schneider MSC: 53A07 52A20 35G10 35K25 PDF BibTeX XML Cite \textit{K. Tso}, Commun. Pure Appl. Math. 38, 867--882 (1985; Zbl 0612.53005) Full Text: DOI
Urbas, John I. E. The equation of prescribed Gauss curvature without boundary conditions. (English) Zbl 0566.53013 J. Differ. Geom. 20, 311-327 (1984). Reviewer: H.Reckziegel MSC: 53A07 35Q99 PDF BibTeX XML Cite \textit{J. I. E. Urbas}, J. Differ. Geom. 20, 311--327 (1984; Zbl 0566.53013) Full Text: DOI
Carneiro de Almeida, Sebastião Minimal hypersurfaces of \(S^ 4\) with non zero Gauss-Kronecker curvature. (English) Zbl 0569.53025 Bol. Soc. Bras. Mat. 14, No. 2, 137-146 (1983). Reviewer: T.Hasanis MSC: 53C42 53A10 PDF BibTeX XML Cite \textit{S. Carneiro de Almeida}, Bol. Soc. Bras. Mat. 14, No. 2, 137--146 (1983; Zbl 0569.53025) Full Text: DOI
Georgiu, Chr.; Hasanis, Th. Ovaloids whose curvatures are powers of support functions. (English) Zbl 0457.53030 Mathematika 28, 192-197 (1981). MSC: 53C45 PDF BibTeX XML Cite \textit{Chr. Georgiu} and \textit{Th. Hasanis}, Mathematika 28, 192--197 (1981; Zbl 0457.53030) Full Text: DOI
Chen, Bang-Yen Notes on the G-Gauss-Kronecker curvature. (English) Zbl 0181.49802 Nanta Math. 2, No. 1, 47-53 (1968). MSC: 53-XX PDF BibTeX XML Cite \textit{B.-Y. Chen}, Nanta Math. 2, No. 1, 47--53 (1968; Zbl 0181.49802)
Chen, Bang-Yen Some integral formulas of the Gauss-Kronecker curvature. (English) Zbl 0165.24602 Kōdai Math. Semin. Rep. 20, 410-413 (1968). MSC: 53-XX PDF BibTeX XML Cite \textit{B.-Y. Chen}, Kōdai Math. Semin. Rep. 20, 410--413 (1968; Zbl 0165.24602) Full Text: DOI