WIAS Preprint No. 1897, (2013)

A curvature estimate for open surfaces subject to a general mean curvature operator and natural contact conditions at their boundary



Authors

  • Druet, Pierre-Étienne
    ORCID: 0000-0001-5303-0500

2010 Mathematics Subject Classification

  • 35J93, 35B65, 58J99

Keywords

  • Mean curvature equation, contact-angle boundary conditions, regularity theory, K-K' quasi-conformal Gaussian map

Abstract

In the seventies, L. Simon showed that the main curvatures of two-dimensional hypersurfaces obeying a general equation of mean curvature type are a priori bounded by the Hölder norm of the coefficients of the surface differential operator. This was an essentially interior estimate. In this paper, we provide a complement to the theory, proving a global curvature estimate for open surfaces that satisfy natural contact conditions at the intersection with a given boundary.

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