Soultanis, Elefterios; Wenger, Stefan Area minimizing surfaces in homotopy classes in metric spaces. (English) Zbl 07542898 Trans. Am. Math. Soc. 375, No. 7, 4711-4739 (2022). MSC: 49Q05 53A10 53C23 PDF BibTeX XML Cite \textit{E. Soultanis} and \textit{S. Wenger}, Trans. Am. Math. Soc. 375, No. 7, 4711--4739 (2022; Zbl 07542898) Full Text: DOI OpenURL
Soultanis, Elefterios Path and quasi-homotopy for Sobolev maps between manifolds. (English) Zbl 1462.58005 J. Funct. Anal. 280, No. 8, Article ID 108935, 23 p. (2021). Reviewer: Mohammed El Aïdi (Bogotá) MSC: 58B05 55P99 46E35 PDF BibTeX XML Cite \textit{E. Soultanis}, J. Funct. Anal. 280, No. 8, Article ID 108935, 23 p. (2021; Zbl 1462.58005) Full Text: DOI arXiv OpenURL
Van Schaftingen, Jean Estimates by gap potentials of free homotopy decompositions of critical Sobolev maps. (English) Zbl 1437.58008 Adv. Nonlinear Anal. 9, 1214-1250 (2020). Reviewer: Hirokazu Nishimura (Tsukuba) MSC: 58C10 46E35 55M25 55P99 55Q25 58A12 PDF BibTeX XML Cite \textit{J. Van Schaftingen}, Adv. Nonlinear Anal. 9, 1214--1250 (2020; Zbl 1437.58008) Full Text: DOI arXiv OpenURL
Convent, Alexandra; Van Schaftingen, Jean Higher order intrinsic weak differentiability and Sobolev spaces between manifolds. (English) Zbl 1417.58008 Adv. Calc. Var. 12, No. 3, 303-332 (2019). MSC: 58D15 PDF BibTeX XML Cite \textit{A. Convent} and \textit{J. Van Schaftingen}, Adv. Calc. Var. 12, No. 3, 303--332 (2019; Zbl 1417.58008) Full Text: DOI arXiv OpenURL
Hopper, Christopher P. Partial regularity for holonomic minimisers of quasiconvex functionals. (English) Zbl 1347.49055 Arch. Ration. Mech. Anal. 222, No. 1, 91-141 (2016). Reviewer: Elvira Mascolo (Firenze) MSC: 49N60 PDF BibTeX XML Cite \textit{C. P. Hopper}, Arch. Ration. Mech. Anal. 222, No. 1, 91--141 (2016; Zbl 1347.49055) Full Text: DOI OpenURL
Brezis, Haïm; Mironescu, Petru Density in \(W^{s, p}(\operatorname{\Omega}; N)\). (English) Zbl 06473109 J. Funct. Anal. 269, No. 7, 2045-2109 (2015). MSC: 35-XX 32-XX 26-XX PDF BibTeX XML Cite \textit{H. Brezis} and \textit{P. Mironescu}, J. Funct. Anal. 269, No. 7, 2045--2109 (2015; Zbl 06473109) Full Text: DOI arXiv OpenURL
Isobe, Takeshi Sobolev bundles with Abelian structure groups. (English) Zbl 1304.46031 Calc. Var. Partial Differ. Equ. 49, No. 1-2, 77-102 (2014). MSC: 46E35 55N30 58E15 PDF BibTeX XML Cite \textit{T. Isobe}, Calc. Var. Partial Differ. Equ. 49, No. 1--2, 77--102 (2014; Zbl 1304.46031) Full Text: DOI OpenURL
Wen, Haomin Lipschitz minimality of the multiplication maps of unit complex, quaternion and octonion numbers. (English) Zbl 1285.53050 Algebr. Geom. Topol. 14, No. 1, 407-420 (2014). Reviewer: Vasile Oproiu (Iaşi) MSC: 53C43 55R25 49Q15 PDF BibTeX XML Cite \textit{H. Wen}, Algebr. Geom. Topol. 14, No. 1, 407--420 (2014; Zbl 1285.53050) Full Text: DOI arXiv OpenURL
Bousquet, Pierre; Ponce, Augusto C.; van Schaftingen, Jean Density of smooth maps for fractional Sobolev spaces \(W^{s, p}\) into \(\ell\) simply connected manifolds when \(s \geq 1\). (English) Zbl 1314.58005 Confluentes Math. 5, No. 2, 3-22 (2013). MSC: 58C25 46E35 46T20 PDF BibTeX XML Cite \textit{P. Bousquet} et al., Confluentes Math. 5, No. 2, 3--22 (2013; Zbl 1314.58005) Full Text: DOI arXiv OpenURL
Gastel, Andreas; Nerf, Andreas J. Minimizing sequences for conformally invariant integrals of higher order. (English) Zbl 1276.58003 Calc. Var. Partial Differ. Equ. 47, No. 3-4, 499-521 (2013). Reviewer: Vladimir Balan (Bucureşti) MSC: 58E20 58D15 PDF BibTeX XML Cite \textit{A. Gastel} and \textit{A. J. Nerf}, Calc. Var. Partial Differ. Equ. 47, No. 3--4, 499--521 (2013; Zbl 1276.58003) Full Text: DOI OpenURL
Goldstein, Paweł; Hajłasz, Piotr Sobolev mappings, degree, homotopy classes and rational homology spheres. (English) Zbl 1262.58010 J. Geom. Anal. 22, No. 2, 320-338 (2012). MSC: 58D15 46E35 46E30 PDF BibTeX XML Cite \textit{P. Goldstein} and \textit{P. Hajłasz}, J. Geom. Anal. 22, No. 2, 320--338 (2012; Zbl 1262.58010) Full Text: DOI arXiv OpenURL
Nakauchi, Nobumitsu; Takenaka, Yumi A variational problem for pullback metrics. (English) Zbl 1254.53095 Ric. Mat. 60, No. 2, 219-235 (2011). MSC: 53C43 58E20 PDF BibTeX XML Cite \textit{N. Nakauchi} and \textit{Y. Takenaka}, Ric. Mat. 60, No. 2, 219--235 (2011; Zbl 1254.53095) Full Text: DOI OpenURL
Nakauchi, Nobumitsu A variational problem related to conformal maps. (English) Zbl 1230.53039 Osaka J. Math. 48, No. 3, 719-741 (2011). Reviewer: Gabjin Yun (Yongin) MSC: 53C21 58E20 53C43 PDF BibTeX XML Cite \textit{N. Nakauchi}, Osaka J. Math. 48, No. 3, 719--741 (2011; Zbl 1230.53039) Full Text: Euclid OpenURL
Lin, Junyu; Ding, Shijin Blow-up solutions to Landau–Lifshitz–Maxwell systems. (English) Zbl 1222.35046 Math. Methods Appl. Sci. 34, No. 8, 1006-1024 (2011). Reviewer: Rainer Picard (Dresden) MSC: 35B44 35Q60 35B65 35K55 PDF BibTeX XML Cite \textit{J. Lin} and \textit{S. Ding}, Math. Methods Appl. Sci. 34, No. 8, 1006--1024 (2011; Zbl 1222.35046) Full Text: DOI OpenURL
Isobe, Takeshi Topological and analytical properties of Sobolev bundles. II. Higher dimensional cases. (English) Zbl 1250.58004 Rev. Mat. Iberoam. 26, No. 3, 729-798 (2010). MSC: 58B20 58D15 46E35 57R22 58E15 PDF BibTeX XML Cite \textit{T. Isobe}, Rev. Mat. Iberoam. 26, No. 3, 729--798 (2010; Zbl 1250.58004) Full Text: DOI Euclid OpenURL
Fuglede, Bent Polyhedra as domains of harmonic maps. (English) Zbl 1206.57027 Topology Appl. 157, No. 5, 815-830 (2010). Reviewer: Jonathan Barmak (Stockholm) MSC: 57Q05 58E20 53C43 49N60 31C12 PDF BibTeX XML Cite \textit{B. Fuglede}, Topology Appl. 157, No. 5, 815--830 (2010; Zbl 1206.57027) Full Text: DOI OpenURL
Isobe, Takeshi Topological and analytical properties of Sobolev bundles. I: The critical case. (English) Zbl 1166.58003 Ann. Global Anal. Geom. 35, No. 3, 277-337 (2009). Reviewer: Paraskevi Tamia-Dimopoulou (Thessaloniki) MSC: 58B20 57N20 58E15 55R10 PDF BibTeX XML Cite \textit{T. Isobe}, Ann. Global Anal. Geom. 35, No. 3, 277--337 (2009; Zbl 1166.58003) Full Text: DOI OpenURL
Mucci, Domenico Strong density results in trace spaces of maps between manifolds. (English) Zbl 1171.58002 Manuscr. Math. 128, No. 4, 421-441 (2009). Reviewer: Andrew Bucki (Edmond) MSC: 58D15 46E35 41A29 PDF BibTeX XML Cite \textit{D. Mucci}, Manuscr. Math. 128, No. 4, 421--441 (2009; Zbl 1171.58002) Full Text: DOI OpenURL
Hajłasz, Piotr Density of Lipschitz mappings in the class of Sobolev mappings between metric spaces. (English) Zbl 1175.46022 Math. Ann. 343, No. 4, 801-823 (2009). Reviewer: Yang Dachun (Beijing) MSC: 46E35 PDF BibTeX XML Cite \textit{P. Hajłasz}, Math. Ann. 343, No. 4, 801--823 (2009; Zbl 1175.46022) Full Text: DOI Link OpenURL
Isobe, Takeshi On global singularities of Sobolev mappings. (English) Zbl 1099.46052 Math. Z. 252, No. 4, 691-730 (2006). Reviewer: Messoud A. Efendiev (Berlin) MSC: 46T10 46T30 55S35 58D15 PDF BibTeX XML Cite \textit{T. Isobe}, Math. Z. 252, No. 4, 691--730 (2006; Zbl 1099.46052) Full Text: DOI OpenURL
Isobe, Takeshi Obstruction theory for the approximation and the deformation problems for Sobolev mappings. (English) Zbl 1097.46050 Ann. Global Anal. Geom. 27, No. 4, 299-332 (2005). Reviewer: Raymond Johnson (College Park) MSC: 46T10 46T30 55S35 58D15 PDF BibTeX XML Cite \textit{T. Isobe}, Ann. Global Anal. Geom. 27, No. 4, 299--332 (2005; Zbl 1097.46050) Full Text: DOI OpenURL
Taheri, Ali Local minimizers and quasiconvexity – the impact of topology. (English) Zbl 1073.49007 Arch. Ration. Mech. Anal. 176, No. 3, 363-414 (2005). MSC: 49J45 49J10 58E05 PDF BibTeX XML Cite \textit{A. Taheri}, Arch. Ration. Mech. Anal. 176, No. 3, 363--414 (2005; Zbl 1073.49007) Full Text: DOI OpenURL
Hardt, Robert; Riviére, Tristan Connecting topological Hopf singularities. (English) Zbl 1150.58004 Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 2, No. 2, 287-344 (2003). Reviewer: Andrew Bucki (Edmond) MSC: 58D15 58E20 49Q15 PDF BibTeX XML Cite \textit{R. Hardt} and \textit{T. Riviére}, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 2, No. 2, 287--344 (2003; Zbl 1150.58004) Full Text: EuDML OpenURL
Hang, Fengbo; Lin, Fanghua Topology of Sobolev mappings. II. (English) Zbl 1061.46032 Acta Math. 191, No. 1, 55-107 (2003). Reviewer: Raymond Johnson (College Park) MSC: 46E35 58D15 58C99 PDF BibTeX XML Cite \textit{F. Hang} and \textit{F. Lin}, Acta Math. 191, No. 1, 55--107 (2003; Zbl 1061.46032) Full Text: DOI OpenURL
Hajłasz, Piotr; Malý, Jan Approximation in Sobolev spaces of nonlinear expressions involving the gradient. (English) Zbl 1029.46028 Ark. Mat. 40, No. 2, 245-274 (2002). Reviewer: Joan Cerda (Barcelona) MSC: 46E35 PDF BibTeX XML Cite \textit{P. Hajłasz} and \textit{J. Malý}, Ark. Mat. 40, No. 2, 245--274 (2002; Zbl 1029.46028) Full Text: DOI OpenURL
Brezis, Haim; Li, Yanyan Topology and Sobolev spaces. (English) Zbl 1001.46019 J. Funct. Anal. 183, No. 2, 321-369 (2001). Reviewer: Julian Musielak (Poznań) MSC: 46E35 PDF BibTeX XML Cite \textit{H. Brezis} and \textit{Y. Li}, J. Funct. Anal. 183, No. 2, 321--369 (2001; Zbl 1001.46019) Full Text: DOI Link OpenURL
Almeida, Luís; Bethuel, Fabrice Topological methods for the Ginzburg-Landau equations. (English) Zbl 0904.35023 J. Math. Pures Appl., IX. Sér. 77, No. 1, 1-49 (1998). Reviewer: S.Sakaguchi (Ehime) MSC: 35J65 35J20 82B26 PDF BibTeX XML Cite \textit{L. Almeida} and \textit{F. Bethuel}, J. Math. Pures Appl. (9) 77, No. 1, 1--49 (1998; Zbl 0904.35023) Full Text: DOI OpenURL
Thalmaier, Anton Brownian motion and the formation of singularities in the heat flow for harmonic maps. (English) Zbl 0846.58056 Probab. Theory Relat. Fields 105, No. 3, 335-367 (1996). Reviewer: A.Thalmaier (Regensburg) MSC: 58J65 58J35 60H30 58E20 PDF BibTeX XML Cite \textit{A. Thalmaier}, Probab. Theory Relat. Fields 105, No. 3, 335--367 (1996; Zbl 0846.58056) Full Text: DOI OpenURL
Baldo, Sisto; Orlandi, Giandomenico Homotopy types for tamely approximable Sobolev maps between manifolds. (English) Zbl 0884.58030 Calc. Var. Partial Differ. Equ. 4, No. 4, 369-384 (1996). Reviewer: C.S.Sharma (London) MSC: 58E15 49Q20 58D15 PDF BibTeX XML Cite \textit{S. Baldo} and \textit{G. Orlandi}, Calc. Var. Partial Differ. Equ. 4, No. 4, 369--384 (1996; Zbl 0884.58030) Full Text: DOI OpenURL
Elworthy, K. D.; Rosenberg, S. Homotopy and homology vanishing theorems and the stability of stochastic flows. (English) Zbl 0858.58053 Geom. Funct. Anal. 6, No. 1, 51-78 (1996). Reviewer: H.Crauel (Saarbrücken) MSC: 58J65 60H15 57N65 PDF BibTeX XML Cite \textit{K. D. Elworthy} and \textit{S. Rosenberg}, Geom. Funct. Anal. 6, No. 1, 51--78 (1996; Zbl 0858.58053) Full Text: DOI arXiv EuDML OpenURL
Bethuel, Fabrice Approximations in trace spaces defined between manifolds. (English) Zbl 0824.58011 Nonlinear Anal., Theory Methods Appl. 24, No. 1, 121-130 (1995). Reviewer: Th.M.Rassias (Athens) MSC: 58C25 PDF BibTeX XML Cite \textit{F. Bethuel}, Nonlinear Anal., Theory Methods Appl. 24, No. 1, 121--130 (1995; Zbl 0824.58011) Full Text: DOI OpenURL
Hajłasz, Piotr Equivalent statement of the Poincaré conjecture. (English) Zbl 0820.46027 Ann. Mat. Pura Appl., IV. Ser. 167, 25-31 (1994). Reviewer: E.Outerelo (Madrid) MSC: 46E35 58D15 57M40 PDF BibTeX XML Cite \textit{P. Hajłasz}, Ann. Mat. Pura Appl. (4) 167, 25--31 (1994; Zbl 0820.46027) Full Text: DOI OpenURL
Wei, S. Walter; Yau, Chi-Ming Regularity of \(p\)-energy minimizing maps and \(p\)-superstrongly unstable indices. (English) Zbl 0851.58014 J. Geom. Anal. 4, No. 2, 247-272 (1994). MSC: 58E20 58E30 PDF BibTeX XML Cite \textit{S. W. Wei} and \textit{C.-M. Yau}, J. Geom. Anal. 4, No. 2, 247--272 (1994; Zbl 0851.58014) Full Text: DOI OpenURL
Giaquinta, M.; Modica, G.; Souček, J. Graphs of finite mass which cannot be approximated in area by smooth graphs. (English) Zbl 0796.58006 Manuscr. Math. 78, No. 3, 259-271 (1993). Reviewer: D.Motreanu (Iaşi) MSC: 58C06 46G10 PDF BibTeX XML Cite \textit{M. Giaquinta} et al., Manuscr. Math. 78, No. 3, 259--271 (1993; Zbl 0796.58006) Full Text: DOI EuDML OpenURL
Nakauchi, Nobumitsu Homomorphism between homotopy groups induced by elements of the Sobolev space \(L^{1,p}(M,N)\). (English) Zbl 0806.57023 Manuscr. Math. 78, No. 1, 1-7 (1993). MSC: 57R99 58C99 55Q99 PDF BibTeX XML Cite \textit{N. Nakauchi}, Manuscr. Math. 78, No. 1, 1--7 (1993; Zbl 0806.57023) Full Text: DOI EuDML OpenURL
Giaquinta, M.; Modica, G.; Souček, J. The Dirichlet integral for mappings between manifolds: Cartesian currents and homology. (English) Zbl 0762.49018 Math. Ann. 294, No. 2, 325-386 (1992). Reviewer: M.Giaquinta (Firenze) MSC: 49Q20 PDF BibTeX XML Cite \textit{M. Giaquinta} et al., Math. Ann. 294, No. 2, 325--386 (1992; Zbl 0762.49018) Full Text: DOI EuDML OpenURL
Giaquinta, Mariano; Modica, Giuseppe; Souček, Jiří Area and the area formula. (English) Zbl 0828.49022 Rend. Semin. Mat. Fis. Milano 62, 53-87 (1992). Reviewer: Reinhardt Euler (Brest) MSC: 49Q15 PDF BibTeX XML Cite \textit{M. Giaquinta} et al., Rend. Semin. Mat. Fis. Milano 62, 53--87 (1992; Zbl 0828.49022) Full Text: DOI OpenURL
Bethuel, Fabrice The approximation problem for Sobolev maps between two manifolds. (English) Zbl 0756.46017 Acta Math. 167, No. 3-4, 153-206 (1991). Reviewer: C.S.Sharma (London) MSC: 46E35 58D15 54C35 PDF BibTeX XML Cite \textit{F. Bethuel}, Acta Math. 167, No. 3--4, 153--206 (1991; Zbl 0756.46017) Full Text: DOI OpenURL
Fuchs, Martin p-harmonic obstacle problems. I: Partial regularity theory. (English) Zbl 0715.49003 Ann. Mat. Pura Appl., IV. Ser. 156, 127-158 (1990). MSC: 49J10 49J40 49N60 35J85 58E20 PDF BibTeX XML Cite \textit{M. Fuchs}, Ann. Mat. Pura Appl. (4) 156, 127--158 (1990; Zbl 0715.49003) Full Text: DOI OpenURL
Bethuel, F. A characterization of maps in \(H^ 1(B^ 3,S^ 2)\) which can be approximated by smooth maps. (English) Zbl 0708.58004 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 7, No. 4, 269-286 (1990). Reviewer: J.Durdil MSC: 58C25 46E35 PDF BibTeX XML Cite \textit{F. Bethuel}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 7, No. 4, 269--286 (1990; Zbl 0708.58004) Full Text: DOI Numdam EuDML OpenURL
Chen, Yunmei; Ding, Weiyue Blow-up and global existence for heat flows of harmonic maps. (English) Zbl 0674.58019 Invent. Math. 99, No. 3, 567-578 (1990). Reviewer: Chen Yunmei MSC: 58E99 58E20 PDF BibTeX XML Cite \textit{Y. Chen} and \textit{W. Ding}, Invent. Math. 99, No. 3, 567--578 (1990; Zbl 0674.58019) Full Text: DOI EuDML OpenURL
Fuchs, Martin p-harmonic obstacle problems. II: Extensions of maps and applications. (English) Zbl 0715.49004 Manuscr. Math. 63, No. 4, 381-419 (1989). MSC: 49J10 49J40 49N60 35J85 58E20 35R35 PDF BibTeX XML Cite \textit{M. Fuchs}, Manuscr. Math. 63, No. 4, 381--419 (1989; Zbl 0715.49004) Full Text: DOI EuDML OpenURL
Bethuel, Fabrice; Zheng, Xiaomin Density of smooth functions between two manifolds in Sobolev spaces. (English) Zbl 0657.46027 J. Funct. Anal. 80, No. 1, 60-75 (1988). Reviewer: J.Włoka MSC: 46E35 PDF BibTeX XML Cite \textit{F. Bethuel} and \textit{X. Zheng}, J. Funct. Anal. 80, No. 1, 60--75 (1988; Zbl 0657.46027) Full Text: DOI OpenURL
White, Brian Homotopy classes in Sobolev spaces and the existence of energy minimizing maps. (English) Zbl 0647.58016 Acta Math. 160, No. 1-2, 1-17 (1988). Reviewer: P.Mattila MSC: 58E30 58B05 PDF BibTeX XML Cite \textit{B. White}, Acta Math. 160, No. 1--2, 1--17 (1988; Zbl 0647.58016) Full Text: DOI OpenURL
Croke, Christopher B. Lower bounds on the energy of maps. (English) Zbl 0634.53042 Duke Math. J. 55, 901-908 (1987). Reviewer: Th.Friedrich MSC: 53C42 53C22 PDF BibTeX XML Cite \textit{C. B. Croke}, Duke Math. J. 55, 901--908 (1987; Zbl 0634.53042) Full Text: DOI OpenURL
Howard, Ralph; Wei, S. Walter Nonexistence of stable harmonic maps to and from certain homogeneous spaces and submanifolds of Euclidean space. (English) Zbl 0588.58015 Trans. Am. Math. Soc. 294, 319-331 (1986). MSC: 58E20 53C35 53A07 PDF BibTeX XML Cite \textit{R. Howard} and \textit{S. W. Wei}, Trans. Am. Math. Soc. 294, 319--331 (1986; Zbl 0588.58015) Full Text: DOI OpenURL
White, Brian Homotopy classes in Sobolev spaces and energy minimizing maps. (English) Zbl 0595.58011 Bull. Am. Math. Soc., New Ser. 13, 166-168 (1985). Reviewer: Shen Yibing MSC: 58E20 55P10 46E35 PDF BibTeX XML Cite \textit{B. White}, Bull. Am. Math. Soc., New Ser. 13, 166--168 (1985; Zbl 0595.58011) Full Text: DOI OpenURL