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arXiv · 1308.1931

The evolution of H-surfaces with a Plateau boundary condition

Frank Duzaar·Christoph Scheven
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Abstract

In this paper we consider the heat flow associated to the classical Plateau problem for surfaces of prescribed mean curvature. We show that an isoperimetric condition on H ensures the existence of a global weak solution. Moreover, we establish that these global solutions sub-converge, as time tends to infinity, to a conformal solution of the classical Plateau problem for surfaces of prescribed mean curvature.

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Frank Duzaar, Christoph Scheven. 2013-08-08. The evolution of H-surfaces with a Plateau boundary condition. https://doi.org/10.1016/j.anihpc.2013.10.003

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