The Mean Curvature Equation in Pseudohermitian Geometry.
November 02, 2005 11:00 AM to 12:00 PM
Speakers:
Cheng, Jih-Hsin
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Abstract: |
I will make a brief report on the recent study about the mean curvature equation in pseudohermitian geometry. As a differential equation, this (p-)minimal surface equation is degenerate (hyperbolic and elliptic) in dimension 2 while subelliptic in the nonsingular domain for higher dimensions. We analyze the singular set and formulate an extension theorem. This allows us to classify the entire solutions to this equation and to solve a Bernstein-type problem. As a geometric application, we prove the nonexistence of C^{2} smooth hyperbolic surfaces having bounded p-mean curvature, immersed in a pseudohermitian 3-manifold. From the variational formulation of the equation, we study the Dirichlet problem by proving the existence and the uniqueness of the (p-)minimizers. |
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