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S. Winklmann

Maximum principles for energy stationary hypersurfaces

Keywords: maximum principle, singular variational problem, enclosure theorem, critical immersion, curvature flow

We consider critical immersions of singular variational integrals of the type E_α(X) = ∫_M X_{n + 1}^α dA, α > 0. We construct quadratic forms which are subharmonic on any stationary hypersurface using methods of Dierkes [4] and Hildebrandt [9]. This leads to enclosure theorems which generalize well-known results of Böhme, Hildebrandt, and Tausch [2] for minimal surfaces under gravitational forces. Finally, we discuss the application of these estimates to the corresponding curvature flow problem.

Analysis, Oldenbourg Wissenschaftsverlag

Print ISSN: 0174-4747
Volume: 26, 02/2006
Pages: 251 - 258

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