Duan, Huagui; Liu, Hui; Long, Yiming; Wang, Wei Generalized common index jump theorem with applications to closed characteristics on star-shaped hypersurfaces and beyond. (English) Zbl 07807087 J. Funct. Anal. 286, No. 7, Article ID 110352, 41 p. (2024). MSC: 53A07 53C22 58E05 37J46 34C25 PDFBibTeX XMLCite \textit{H. Duan} et al., J. Funct. Anal. 286, No. 7, Article ID 110352, 41 p. (2024; Zbl 07807087) Full Text: DOI arXiv
Hu, Xijun; Long, Yiming; Ou, Yuwei Linear stability of the elliptic relative equilibrium with \((1 + n)\)-gon central configurations in planar \(n\)-body problem. (English) Zbl 1437.37066 Nonlinearity 33, No. 3, 1016-1045 (2020). Reviewer: Martha Alvarez-Ramirez (México City) MSC: 37J25 70F10 53D12 PDFBibTeX XMLCite \textit{X. Hu} et al., Nonlinearity 33, No. 3, 1016--1045 (2020; Zbl 1437.37066) Full Text: DOI arXiv
Liu, Hui; Long, Yiming; Xiao, Yuming The existence of two non-contractible closed geodesics on every bumpy Finsler compact space form. (English) Zbl 1423.53053 Discrete Contin. Dyn. Syst. 38, No. 8, 3803-3829 (2018). Reviewer: Oana Constantinescu (Iaşi) MSC: 53C22 58E05 58E10 53C60 PDFBibTeX XMLCite \textit{H. Liu} et al., Discrete Contin. Dyn. Syst. 38, No. 8, 3803--3829 (2018; Zbl 1423.53053) Full Text: DOI arXiv
Zhou, Qinglong; Long, Yiming Maslov-type indices and linear stability of elliptic Euler solutions of the three-body problem. (English) Zbl 1382.35293 Arch. Ration. Mech. Anal. 226, No. 3, 1249-1301 (2017). Reviewer: Thomas Ernst (Uppsala) MSC: 35Q70 70F07 35B35 53D12 PDFBibTeX XMLCite \textit{Q. Zhou} and \textit{Y. Long}, Arch. Ration. Mech. Anal. 226, No. 3, 1249--1301 (2017; Zbl 1382.35293) Full Text: DOI arXiv
Duan, Huagui; Long, Yiming; Wang, Wei The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds. (English) Zbl 1381.53071 Calc. Var. Partial Differ. Equ. 55, No. 6, Paper No. 145, 28 p. (2016). Reviewer: Hans-Bert Rademacher (Leipzig) MSC: 53C22 58E05 58E10 53C60 PDFBibTeX XMLCite \textit{H. Duan} et al., Calc. Var. Partial Differ. Equ. 55, No. 6, Paper No. 145, 28 p. (2016; Zbl 1381.53071) Full Text: DOI arXiv
Duan, Huagui; Long, Yiming; Wang, Wei Two closed geodesics on compact simply connected bumpy Finsler manifolds. (English) Zbl 1357.53086 J. Differ. Geom. 104, No. 2, 275-289 (2016). Reviewer: Nicoleta Aldea (Brasov) MSC: 53C60 53C22 58E10 58E05 PDFBibTeX XMLCite \textit{H. Duan} et al., J. Differ. Geom. 104, No. 2, 275--289 (2016; Zbl 1357.53086) Full Text: DOI Link
Duan, Huagui; Long, Yiming; Xiao, Yuming Two closed geodesics on \(\mathbb RP^{2n+1}\) with a bumpy Finsler metric. (English) Zbl 1330.53096 Calc. Var. Partial Differ. Equ. 54, No. 3, 2883-2894 (2015). Reviewer: Lajos Tamássy (Debrecen) MSC: 53C60 53C22 58E05 58E10 PDFBibTeX XMLCite \textit{H. Duan} et al., Calc. Var. Partial Differ. Equ. 54, No. 3, 2883--2894 (2015; Zbl 1330.53096) Full Text: DOI
Xiao, Yuming; Long, Yiming Topological structure of non-contractible loop space and closed geodesics on real projective spaces with odd dimensions. (English) Zbl 1351.37153 Adv. Math. 279, 159-200 (2015). MSC: 37D40 58E10 53C22 PDFBibTeX XMLCite \textit{Y. Xiao} and \textit{Y. Long}, Adv. Math. 279, 159--200 (2015; Zbl 1351.37153) Full Text: DOI arXiv
Long, Yiming Recent progress on closed geodesics in some compact simply connected manifolds. (English) Zbl 1473.53063 Liu, Chungen (ed.) et al., Progress in variational methods. Proceedings of the 2nd international conference on variational methods (ICVAM-2), Nankai University, Tianjin, China, May 18–22, 2009. Hackensack, NJ: World Scientific. Nankai Ser. Pure Appl. Math. Theor. Phys. 7, 107-125 (2011). MSC: 53C22 53C60 PDFBibTeX XMLCite \textit{Y. Long}, Nankai Ser. Pure Appl. Math. Theor. Phys. 7, 107--125 (2011; Zbl 1473.53063) Full Text: Link
Liu, Chungen (ed.); Long, Yiming (ed.) Progress in variational methods. Proceedings of the 2nd international conference on variational methods (ICVAM-2), Nankai University, Tianjin, China, May 18–22, 2009. (English) Zbl 1237.58002 Nankai Series in Pure, Applied Mathematics and Theoretical Physics 7. Hackensack, NJ: World Scientific (ISBN 978-981-4327-83-1/hbk; 978-981-4327-84-8/ebook). x, 238 p. (2011). MSC: 58-06 58E30 57R70 53C21 37J05 00B25 PDFBibTeX XMLCite \textit{C. Liu} (ed.) and \textit{Y. Long} (ed.), Progress in variational methods. Proceedings of the 2nd international conference on variational methods (ICVAM-2), Nankai University, Tianjin, China, May 18--22, 2009. Hackensack, NJ: World Scientific (2011; Zbl 1237.58002) Full Text: Link
Duan, Huagui; Long, Yiming The index growth and multiplicity of closed geodesics. (English) Zbl 1206.53043 J. Funct. Anal. 259, No. 7, 1850-1913 (2010). Reviewer: Ben McKay (Cork) MSC: 53C22 58E10 53C40 PDFBibTeX XMLCite \textit{H. Duan} and \textit{Y. Long}, J. Funct. Anal. 259, No. 7, 1850--1913 (2010; Zbl 1206.53043) Full Text: DOI arXiv
Bangert, Victor; Long, Yiming The existence of two closed geodesics on every Finsler 2-sphere. (English) Zbl 1187.53040 Math. Ann. 346, No. 2, 335-366 (2010). Reviewer: Marco Abate (Pisa) MSC: 53C22 53C60 37J45 58E10 PDFBibTeX XMLCite \textit{V. Bangert} and \textit{Y. Long}, Math. Ann. 346, No. 2, 335--366 (2010; Zbl 1187.53040) Full Text: DOI arXiv
Duan, Huagui; Long, Yiming The index quasi-periodicity and multiplicity of closed geodesics. arXiv:1008.1458 Preprint, arXiv:1008.1458 [math.SG] (2010). MSC: 53C22 58E05 58E10 BibTeX Cite \textit{H. Duan} and \textit{Y. Long}, ``The index quasi-periodicity and multiplicity of closed geodesics'', Preprint, arXiv:1008.1458 [math.SG] (2010) Full Text: arXiv OA License
Duan, Huagui; Long, Yiming Morse concavity for closed geodesics. (English) Zbl 1212.58010 Acta Math. Sci., Ser. B, Engl. Ed. 29, No. 3, 731-750 (2009). Reviewer: A. Bucki (Langston) MSC: 58E10 53C22 58E05 PDFBibTeX XMLCite \textit{H. Duan} and \textit{Y. Long}, Acta Math. Sci., Ser. B, Engl. Ed. 29, No. 3, 731--750 (2009; Zbl 1212.58010) Full Text: DOI
Long, Yiming; Duan, Huagui Multiple closed geodesics on 3-spheres. (English) Zbl 1172.53027 Adv. Math. 221, No. 6, 1757-1803 (2009). Reviewer: Ben McKay (Cork) MSC: 53C22 58E10 53C60 PDFBibTeX XMLCite \textit{Y. Long} and \textit{H. Duan}, Adv. Math. 221, No. 6, 1757--1803 (2009; Zbl 1172.53027) Full Text: DOI
Long, Yiming; Wang, Wei Morse indices of closed geodesics on Katok’s 2-spheres. (English) Zbl 1197.58003 Adv. Nonlinear Stud. 8, No. 3, 569-572 (2008). Reviewer: Hans-Bert Rademacher (Leipzig) MSC: 58E10 53C22 53C60 58E05 PDFBibTeX XMLCite \textit{Y. Long} and \textit{W. Wang}, Adv. Nonlinear Stud. 8, No. 3, 569--572 (2008; Zbl 1197.58003) Full Text: DOI
Long, Yiming Collection of problems proposed at International Conference on Variational Methods. (English) Zbl 1147.53002 Front. Math. China 3, No. 2, 259-273 (2008). MSC: 53-02 49-02 00A07 58E05 35A15 34A34 PDFBibTeX XMLCite \textit{Y. Long}, Front. Math. China 3, No. 2, 259--273 (2008; Zbl 1147.53002) Full Text: DOI
Long, Yiming; Wang, Wei Stability of closed geodesics on Finsler 2-spheres. (English) Zbl 1151.53037 J. Funct. Anal. 255, No. 3, 620-641 (2008). Reviewer: Mihai Anastasiei (Iaşi) MSC: 53C22 53C60 PDFBibTeX XMLCite \textit{Y. Long} and \textit{W. Wang}, J. Funct. Anal. 255, No. 3, 620--641 (2008; Zbl 1151.53037) Full Text: DOI
Duan, Huagui; Long, Yiming Multiplicity and stability of closed geodesics on bumpy Finsler 3-spheres. (English) Zbl 1165.53052 Calc. Var. Partial Differ. Equ. 31, No. 4, 483-496 (2008). Reviewer: Adrian Sandovici (Piatra Neamt) MSC: 53C60 53C22 37J45 PDFBibTeX XMLCite \textit{H. Duan} and \textit{Y. Long}, Calc. Var. Partial Differ. Equ. 31, No. 4, 483--496 (2008; Zbl 1165.53052) Full Text: DOI arXiv
Long, Yiming; Wang, Wei Multiple closed geodesics on Riemannian 3-spheres. (English) Zbl 1125.58005 Calc. Var. Partial Differ. Equ. 30, No. 2, 183-214 (2007). Reviewer: Vladimir Balan (Bucureşti) MSC: 58E10 53C22 37C27 PDFBibTeX XMLCite \textit{Y. Long} and \textit{W. Wang}, Calc. Var. Partial Differ. Equ. 30, No. 2, 183--214 (2007; Zbl 1125.58005) Full Text: DOI
Duan, Huagui; Long, Yiming Multiple closed geodesics on bumpy Finsler \(n\)-spheres. (English) Zbl 1106.53048 J. Differ. Equations 233, No. 1, 221-240 (2007). MSC: 53C60 53C22 PDFBibTeX XMLCite \textit{H. Duan} and \textit{Y. Long}, J. Differ. Equations 233, No. 1, 221--240 (2007; Zbl 1106.53048) Full Text: DOI arXiv
Long, Yiming Multiplicity and stability of closed geodesics on Finsler 2-spheres. (English) Zbl 1099.53036 J. Eur. Math. Soc. (JEMS) 8, No. 2, 341-353 (2006). Reviewer: Vladimir Balan (Bucureşti) MSC: 53C22 58E10 58E05 53C60 PDFBibTeX XMLCite \textit{Y. Long}, J. Eur. Math. Soc. (JEMS) 8, No. 2, 341--353 (2006; Zbl 1099.53036) Full Text: DOI
Zhou, Congyi; Long, Yiming Homology classes of the circle space on spheres and the discontinuity of deformations. (English) Zbl 1075.58008 Adv. Nonlinear Stud. 5, No. 1, 1-11 (2005). Reviewer: Vladimir Balan (Bucureşti) MSC: 58E10 58E05 55M30 53C20 PDFBibTeX XMLCite \textit{C. Zhou} and \textit{Y. Long}, Adv. Nonlinear Stud. 5, No. 1, 1--11 (2005; Zbl 1075.58008) Full Text: DOI
Dong, Yujun; Long, Yiming Closed characteristics on asymmetric convex hypersurfaces in \(\mathbb{R}^{2n}\) and the corresponding pinching conditions. (English) Zbl 1073.53010 Acta Math. Sin., Engl. Ser. 20, No. 2, 223-232 (2004). Reviewer: Carla Peri (Milano-Largo) MSC: 53A07 52A20 PDFBibTeX XMLCite \textit{Y. Dong} and \textit{Y. Long}, Acta Math. Sin., Engl. Ser. 20, No. 2, 223--232 (2004; Zbl 1073.53010) Full Text: DOI
Dong, Yujun; Long, Yiming Closed characteristics on partially symmetric compact convex hypersurfaces in \(\mathbb R^{2n}\). (English) Zbl 1109.37048 J. Differ. Equations 196, No. 1, 226-248 (2004). MSC: 37J45 53D05 58E05 PDFBibTeX XMLCite \textit{Y. Dong} and \textit{Y. Long}, J. Differ. Equations 196, No. 1, 226--248 (2004; Zbl 1109.37048) Full Text: DOI
Hu, Xijun; Long, Yiming Closed characteristics on non-degenerate star-shaped hypersurfaces in \(\mathbb R^{2n}\). (English) Zbl 1099.37047 Sci. China, Ser. A 45, No. 8, 1038-1052 (2002). MSC: 37J45 34C25 53D12 58E05 PDFBibTeX XMLCite \textit{X. Hu} and \textit{Y. Long}, Sci. China, Ser. A 45, No. 8, 1038--1052 (2002; Zbl 1099.37047) Full Text: DOI
Long, Yiming Index theory for symplectic paths with applications. (English) Zbl 1012.37012 Progress in Mathematics (Boston, Mass.). 207. Basel: Birkhäuser. xxiv, 380 p. (2002). Reviewer: Roman Srzednicki (Krakow) MSC: 37B30 58E05 37J05 70H05 37-02 70H03 53D12 34C25 PDFBibTeX XMLCite \textit{Y. Long}, Index theory for symplectic paths with applications. Basel: Birkhäuser (2002; Zbl 1012.37012)
Liu, Chun-gen; Long, Yiming; Zhu, Chaofeng Multiplicity of closed characteristics on symmetric convex hypersurfaces in \(\mathbb{R}^{2n}\). (English) Zbl 1005.37030 Math. Ann. 323, No. 2, 201-215 (2002). Reviewer: Jacobo Pejsachowicz (Torino) MSC: 37J45 53C44 34C25 PDFBibTeX XMLCite \textit{C.-g. Liu} et al., Math. Ann. 323, No. 2, 201--215 (2002; Zbl 1005.37030) Full Text: DOI arXiv
Liu, Chungen; Long, Yiming Iterated index formulae for closed geodesics with applications. (English) Zbl 1054.53063 Sci. China, Ser. A 45, No. 1, 9-28 (2002). MSC: 53C22 58E10 PDFBibTeX XMLCite \textit{C. Liu} and \textit{Y. Long}, Sci. China, Ser. A 45, No. 1, 9--28 (2002; Zbl 1054.53063)
Long, Yiming; Zhu, Chaofeng Closed characteristics on compact convex hypersurfaces in \(\mathbb{R}^{2n}\). (English) Zbl 1028.53003 Ann. Math. (2) 155, No. 2, 317-368 (2002). Reviewer: A.A.Borisenko (Khar’kov) MSC: 53A07 52A20 53C45 PDFBibTeX XMLCite \textit{Y. Long} and \textit{C. Zhu}, Ann. Math. (2) 155, No. 2, 317--368 (2002; Zbl 1028.53003) Full Text: DOI arXiv
Long, Yiming; Zhu, Chaofeng Differentiable structure of \(\omega\)-subsets of symplectic groups. (English) Zbl 0994.53031 Sci. China, Ser. A 44, No. 5, 545-554 (2001). MSC: 53D12 37J05 PDFBibTeX XMLCite \textit{Y. Long} and \textit{C. Zhu}, Sci. China, Ser. A 44, No. 5, 545--554 (2001; Zbl 0994.53031) Full Text: DOI
Long, Yiming Dynamics on compact convex hypersurfaces in \(\mathbb{R}^{2n}\). (English) Zbl 1193.37084 Chang, Kung-Ching (ed.) et al., Progress in nonlinear analysis. Proceedings of the second international conference on nonlinear analysis, Tianjin, China, June 14–19, 1999. Singapore: World Scientific (ISBN 981-02-4329-4/hbk). Nankai Ser. Pure Appl. Math. Theor. Phys. 6, 271-288 (2000). MSC: 37J45 34C25 53D12 PDFBibTeX XMLCite \textit{Y. Long}, Nankai Ser. Pure Appl. Math. Theor. Phys. 6, 271--288 (2000; Zbl 1193.37084)
Liu, Chungen; Long, Yiming Iteration inequalities of the Maslov-type index theory with applications. (English) Zbl 0961.37017 J. Differ. Equations 165, No. 2, 355-376 (2000). Reviewer: Paolo Piccione (São Paulo) MSC: 37J10 53D12 PDFBibTeX XMLCite \textit{C. Liu} and \textit{Y. Long}, J. Differ. Equations 165, No. 2, 355--376 (2000; Zbl 0961.37017) Full Text: DOI
Long, Yiming Precise iteration formulae of the Maslov-type index theory and ellipticity of closed characteristics. (English) Zbl 0970.37013 Adv. Math. 154, No. 1, 76-131 (2000). Reviewer: Willy Sarlet (Gent) MSC: 37B30 37J05 53D12 PDFBibTeX XMLCite \textit{Y. Long}, Adv. Math. 154, No. 1, 76--131 (2000; Zbl 0970.37013) Full Text: DOI
Long, Yiming; Zhu, Chaofeng Maslov-type index theory for symplectic paths and spectral flow. II. (English) Zbl 0959.58017 Chin. Ann. Math., Ser. B 21, No. 1, 89-108 (2000). Reviewer: Peter Haskell (Blacksburg) MSC: 58E05 37J45 58J30 53D12 34C25 47A50 PDFBibTeX XMLCite \textit{Y. Long} and \textit{C. Zhu}, Chin. Ann. Math., Ser. B 21, No. 1, 89--108 (2000; Zbl 0959.58017) Full Text: DOI
Zhu, Chaofeng; Long, Yiming Maslov-type index theory for symplectic paths and spectral flow. I. (English) Zbl 0959.58016 Chin. Ann. Math., Ser. B 20, No. 4, 413-424 (1999). Reviewer: Peter Haskell (Blacksburg) MSC: 58E05 58J30 53D12 PDFBibTeX XMLCite \textit{C. Zhu} and \textit{Y. Long}, Chin. Ann. Math., Ser. B 20, No. 4, 413--424 (1999; Zbl 0959.58016) Full Text: DOI
Liu, Chungen; Long, Yiming An optimal increasing estimate of the iterated Maslov-type indices. (English) Zbl 1002.53055 Chin. Sci. Bull. 43, No. 13, 1063-1066 (1998). Reviewer: Luc Vrancken (Utrecht) MSC: 53D12 37J05 PDFBibTeX XMLCite \textit{C. Liu} and \textit{Y. Long}, Chin. Sci. Bull. 43, No. 13, 1063--1066 (1998; Zbl 1002.53055) Full Text: DOI
An, Tianqing; Long, Yiming The classification of exponential paths in \(\text{Sp}(2)\). (English) Zbl 1054.53508 Adv. Math., Beijing 27, No. 3, 209-213 (1998). MSC: 53D12 PDFBibTeX XMLCite \textit{T. An} and \textit{Y. Long}, Adv. Math., Beijing 27, No. 3, 209--213 (1998; Zbl 1054.53508)
Long, Yiming A Maslov-type index theory for symplectic paths. (English) Zbl 0977.53075 Topol. Methods Nonlinear Anal. 10, No. 1, 47-78 (1997). Reviewer: R.Srzednicki (Kraków) MSC: 53D12 37J10 58E05 37B30 PDFBibTeX XMLCite \textit{Y. Long}, Topol. Methods Nonlinear Anal. 10, No. 1, 47--78 (1997; Zbl 0977.53075) Full Text: DOI
Long, Yiming Geodesics in the compactly supported Hamiltonian diffeomorphism group. (English) Zbl 0843.58022 Math. Z. 220, No. 2, 279-294 (1995). Reviewer: Y.Long (Tianjin) MSC: 58E10 58D05 37D40 53D25 37J99 70H05 PDFBibTeX XMLCite \textit{Y. Long}, Math. Z. 220, No. 2, 279--294 (1995; Zbl 0843.58022) Full Text: DOI EuDML