Calculus of Variations and Geometric Measure Theory

G. De Philippis - A. De Rosa - J. Hirsch

The area blow up set for bounded mean curvature submanifolds with respect to elliptic surface energy functionals

created by derosa on 06 Jan 2019
modified on 06 Feb 2019


Published Paper

Inserted: 6 jan 2019
Last Updated: 6 feb 2019

Journal: Discrete Contin. Dyn. Syst.
Year: 2019

ArXiv: 1901.03514 PDF


In this paper we investigate the ''area blow-up'' set of a sequence of smooth co-dimension one manifolds whose first variation with respect to an anisotropic integral is bounded. Following the ideas introduced by White in (J. Differential Geom., 2016), we show that this set has bounded (anisotropic) mean curvature in the viscosity sense. In particular, this allows to show that the set is empty in a variety of situations. As a consequence, we show boundary curvature estimates for two dimensional stable anisotropic minimal surfaces, extending the results of White in (Invent. Math., 1987).