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Research Results
RICARDO SÁ EARP
In a joint work with Eric Toubiana, we study the vertical minimal equation in H^n x R. We find suitable geometric barriers for the Dirichlet problem. The starting point of this work is the discovery of the n-dimensional minimal Scherk type graphs. We obtain the solution of the Dirichlet problem for the minimal equation in H^n x R on a C^0 convex domain of H^n, taking continuous boundary value data on the finite boundary and continuous boundary value data on the asymptotic boundary. In a joint work with Barbara Nelli, University of Aquila, Italy, we prove a vertical half-space theorem for mean curvature ½ surfaces in H^2 x R. We generalize with Pierre Bérard, University of Grenoble, France, a well-known theorem of Lindelöf, investigating the maximum domain of stability of minimal hypersurfaces of revolution, considering other environments different from the Euclidean space. In a joint work with Maria Fernanda Elbert (UFRJ) and Barbara Nelli, we construct examples of vertical graphs of mean curvature H = ½ in H^2 x R over admissible exterior domains in H^2. We study in a individual article the horizontal minimal equation in H^2 x R. We deduce a Bernstein type theorem and we set an open Bernstein type problem in the context of constant mean curvature ≤ ½. Moreover, we deduce for this equation a Radó type result.
RECENT PUBLICATIONS
• Ricardo Sa Earp & Eric Toubiana. Minimal graphs in H^n x R and R^{n+1}. Annales de l'Institut Fourier, 60, n. 7, 2373-2402, 2010. DOI : S 0002-9939(2010)10492-6.
• Ricardo Sa Earp & Pierre Bérard. Lindelöf´s theorem for hyperbolic catenoids. Proceedings of the American Mathematical Society, 138, 3657-3657, 2010. DOI: S 002-9939(2010)10492-6.
• Ricardo Sa Earp & Barbara Nelli. A halfspace theorem for mean curvature H=1/2 surfaces in H^2 x R. Journal of Mathematical Analysis and Applications, 365, 167-170, 2010. DOI: 10.1016/j.jmaa.2009.10.031.
• Ricardo Sa Earp, Maria Fernanda Elbert & Barbara Nelli. Existence of vertical ends of mean curvature 1/2 in H^2 x R. Transactions of the American Mathematical Society, 364, n. 3, 1179-1191, 2012. DOI: S0002- 9947 (2011)05361-4.
• Ricardo Sa Earp. Uniqueness of minimal surfaces whose boundary is a horizontal graph and some Bernstein problems in H^2 x R. Mathematische Zeitschrift, 273, 1, 211-217, 2013. DOI: 10.1007/s00209-012-1001-4.
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