Isolated singularities of the prescribed mean curvature equation in Minkowski 3-space

José A. Gálvez1, Asun Jiménez2, Pablo Mira3
1Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
2Departamento de Geometria, IME, Universidade Federal Fluminense, 24.210-201 Niterói, Brazil
3Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 30203 Cartagena, Murcia, Spain

Tài liệu tham khảo

Akutagawa, 1990, The Gauss map and spacelike surfaces with prescribed mean curvature in Minkowski 3-space, Tohoku Math. J., 42, 67, 10.2748/tmj/1178227694 Bartnik, 1989, Isolated singular points of Lorentzian mean curvature hypersurfaces, Indiana Univ. Math. J., 38, 811, 10.1512/iumj.1989.38.38038 Brander, 2011, Singularities of spacelike constant mean curvature surfaces in Lorentz–Minkowski space, Math. Proc. Camb. Philos. Soc., 150, 527, 10.1017/S0305004111000077 Courant, 1950 Ecker, 1986, Area maximizing hypersurfaces in Minkowski space having an isolated singularity, Manuscr. Math., 56, 375, 10.1007/BF01168501 Estudillo, 1992, Generalized maximal surfaces in Lorentz–Minkowski space L3, Math. Proc. Camb. Philos. Soc., 111, 515, 10.1017/S0305004100075587 Fernández, 2005, The space of complete embedded maximal surfaces with isolated singularities in the 3-dimensional Lorentz–Minkowski space, Math. Ann., 332, 605, 10.1007/s00208-005-0642-6 Fernández, 2007, The moduli space of embedded singly periodic maximal surfaces with isolated singularities in the Lorentz–Minkowski space L3, Manuscr. Math., 122, 439, 10.1007/s00229-007-0079-1 Gálvez, 2005, Embedded isolated singularities of flat surfaces in hyperbolic 3-space, Calc. Var., 24, 239, 10.1007/s00526-004-0321-6 Gálvez, 2015, A classification of isolated singularities of elliptic Monge–Ampère equations in dimension two, Commun. Pure Appl. Math., 68, 2085, 10.1002/cpa.21581 Gálvez, 2016, Isolated singularities of graphs in warped products and Monge–Ampère equations, J. Differ. Equ., 260, 2163, 10.1016/j.jde.2015.09.061 Gilbarg, 2001, Elliptic Partial Differential Equations of Second Order, 10.1007/978-3-642-61798-0 Heinz, 1970, Über das Randverhalten quasilinearer elliptischer Systeme mit isothermen Parametern, Math. Z., 113, 99, 10.1007/BF01141095 Klyachin, 1995, Existence of solutions with singularities for the maximal surface equation in Minkowski space, Russ. Acad. Sci. Sb. Math., 80, 87 Kobayashi, 1984, Maximal surfaces with conelike singularities, J. Math. Soc. Jpn., 36, 609, 10.2969/jmsj/03640609 Müller, 2002, Analyticity of solutions for semilinear elliptic systems of second order, Calc. Var., 15, 257, 10.1007/s005260100127 Nirenberg, 1953, On nonlinear elliptic partial differential equations and Hölder continuity, Commun. Pure Appl. Math., 6, 103, 10.1002/cpa.3160060105 Sauvigny, 1999, Introduction of isothermal parameters into a Riemannian metric by the continuity method, Analysis, 19, 235, 10.1524/anly.1999.19.3.235 Schulz, 1989, Univalent solutions of elliptic systems of Heinz–Lewy type, Ann. Inst. Henri Poincaré, 5, 347, 10.1016/S0294-1449(16)30315-8 Umeda, 2009, Constant-mean-curvature surfaces with singularities in Minkowski 3-space, Exp. Math., 18, 311, 10.1080/10586458.2009.10129050 Umehara, 2006, Maximal surfaces with singularities in Minkowski space, Hokkaido Math. J., 35, 13, 10.14492/hokmj/1285766302