Minimal surfaces in H 2 × R

By Barbara Nelli, H. Rosenberg. 2002

155 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/780d994c6a0e7c353cb9524abdae8c3b53867484

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Citations in the corpus

Infinite boundary value problems for constant mean curvature graphs in ℍ2 × ℝ and S2 × ℝ (2009, methodology): “For H = 0, the Jenkins-Serrin theory was extended to M = H 2 by Nelli and Rosenberg [4] and to arbitrary Riemannian surfaces M by Pinheiro [6].”
GLOBAL PROPERTIES OF CONSTANT MEAN CURVATURE SURFACES IN H 2 ◊R (2006, background): “New examples were produced, as well as many theoretical results; see [Hauswirth 2003; Meeks and Rosenberg 2004; 2005; Nelli and Rosenberg 2002; Rosenberg 2002] for the case H = 0, and [Abresch and Rosenberg 2004; Hoffman et al. 2006; Sá Earp and Toubiana 2004] for the case H 6= 0.”
A Hopf differential for constant mean curvature surfaces inS2×R andH2×R (2004, result): “This collapse is indicated in Figure 3; it is pretty similar to the collapse of the minimal catenoids described in [23, Section 6] or [19].”
The Dirichlet problem for the minimal surface equation, with possible infinite boundary data, over domains in a Riemannian surface (2008, background): “The next results have been proven by Jenkins and Serrin [8] for M = R, by Nelli and Rosenberg [11] when M = H, and by Pinheiro [14] in the general setting.”
General curvature estimates for stable H-surfaces in 3-manifolds applications (2009, unknown): “…not on M , such that for any x ∈ Ω , there exists a harmonic coordinate chart ( U, ϕ, B ( x, r 0 )) , U being an open subset of R 3 containing the origin and B ( x, r 0 ) the geodesic ball in M centered at x of radius r 0 , with ϕ (0) = x , and such that the metric tensor g is C 1 ,α -controlled.”
Totally umbilic surfaces in homogeneous 3-manifolds (2006, unknown): “See for example [14], [6], [7], [17], [15], [12], [13], [11], [9], [4], [2], [10], [5] and [8].”