On the regularity of H-surfaces with free boundaries on a smooth support manifold
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Frank Müller
Abstract
We study surfaces of prescribed mean curvature in R3 with part of their boundaries lying on a support manifold without boundary. We prove C1,μ-regularity of such a surface, whenever the support manifold is of class C2 and the surface itself is a continuous, stationary point of the associated energy functional; consequently, minimizers of that functional are included. In addition, asymptotic expansions near boundary branch points are provided. Our results improve previous work of Hildebrandt and Jäger [HJ] and Hardt [Ha], and generalize corresponding theorems on minimal surfaces. The main difficulty arises from the fact that stationary surfaces with prescribed mean curvature do not have to meet the support manifold perpendicularly, in contrast to minimal surfaces which are stationary points of Dirichlet´s functional.
© by Oldenbourg Wissenschaftsverlag, München, Germany
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- On the regularity of H-surfaces with free boundaries on a smooth support manifold
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Articles in the same Issue
- A generalization of a theorem by Křížek, Luca, and Somer on elite primes
- A uniqueness theorem for meromorphic mappings without counting multiplicities
- On the regularity of H-surfaces with free boundaries on a smooth support manifold
- Schwarz inequality for squares of harmonic conjugate functions
- Two spaces conditions for integrability of the Fourier transform
- An example concerning islands of meromorphic functions and their derivatives
- Nonexistence criteria for polyharmonic boundary-value problems
