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

This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Druet, Pierre-Étienne2016-03-242019-06-2820130946-8633https://doi.org/10.34657/1786https://oa.tib.eu/renate/handle/123456789/3024In 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.application/pdfeng510Mean curvature equationcontact-angle boundary conditionsregularity theoryK - K' quasi-conformal Gaussian mapA curvature estimate for open surfaces subject to a general mean curvature operator and natural contact conditions at their boundaryReport