Geometry & Topology Volume 16, issue 2 (2012)

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The Dirichlet Problem for constant mean curvature graphs in $\mathbb{M}\times\mathbb{R}$

Abigail Folha and Harold Rosenberg

Geometry & Topology 16 (2012) 1171–1203

DOI: 10.2140/gt.2012.16.1171

Bibliography

1	P Collin, H Rosenberg, Construction of harmonic diffeomorphisms and minimal graphs, Ann. of Math. 172 (2010) 1879 MR2726102
2	A Folha, S Melo, The Dirichlet problem for constant mean curvature graphs in $\mathbb{H}\times\mathbb{R}$ over unbounded domains, Pacific J. Math. 251 (2011) 37 MR2794614
3	J A Gálvez, H Rosenberg, Minimal surfaces and harmonic diffeomorphisms from the complex plane onto certain Hadamard surfaces, Amer. J. Math. 132 (2010) 1249 MR2732346
4	D Gilbarg, N S Trudinger, Elliptic partial differential equations of second order, Grundl. Math. Wissen. 224, Springer (1983) MR737190
5	L Hauswirth, H Rosenberg, J Spruck, Infinite boundary value problems for constant mean curvature graphs in $\mathbb{H}^2\times\mathbb{R}$ and $\mathbb{S}^2\times\mathbb{R}$, Amer. J. Math. 131 (2009) 195 MR2488489
6	H Jenkins, J Serrin, Variational problems of minimal surface type. I, Arch. Rational mech. Anal. 12 (1963) 185 MR0145194
7	H Jenkins, J Serrin, Variational problems of minimal surface type II. Boundary value problems for the minimal surface equation, Arch. Rational Mech. Anal. 21 (1966) 321 MR0190811
8	F Labourie, Un lemme de Morse pour les surfaces convexes, Invent. Math. 141 (2000) 239 MR1775215
9	Y Li, L Nirenberg, Regularity of the distance function to the boundary, Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. 29 (2005) 257 MR2305073
10	L Mazet, M M Rodríguez, H Rosenberg, The Dirichlet problem for the minimal surface equation, with possible infinite boundary data, over domains in a Riemannian surface, Proc. Lond. Math. Soc. 102 (2011) 985 MR2806098
11	B Nelli, H Rosenberg, Minimal surfaces in $\mathbb{H}^2\times\mathbb{R}$, Bull. Braz. Math. Soc. 33 (2002) 263 MR1940353
12	A L Pinheiro, A Jenkins–Serrin theorem in $M^2\times\mathbb{R}$, Bull. Braz. Math. Soc. 40 (2009) 117 MR2496117
13	H Rosenberg, Hypersurfaces of constant curvature in space forms, Bull. Sci. Math. 117 (1993) 211 MR1216008
14	H Rosenberg, Minimal surfaces in $\mathbb{M}^2\times\mathbb{R}$, Illinois J. Math. 46 (2002) 1177 MR1988257
15	H Rosenberg, R Souam, E Toubiana, General curvature estimates for stable \hbox$H$–surfaces in $3$–manifolds and applications, J. Differential Geom. 84 (2010) 623 MR2669367
16	J Spruck, Infinite boundary value problems for surfaces of constant mean curvature, Arch. Rational Mech. Anal. 49 (1972) 1 MR0334010
17	J Spruck, Interior gradient estimates and existence theorems for constant mean curvature graphs in $M^n\times R$, Pure Appl. Math. Q. 3 (2007) 785 MR2351645