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 [12], 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 [10].
The area blow up set for bounded mean curvature submanifolds with respect to elliptic surface energy functionals / De Philippis, G.; De Rosa, A.; Hirsch, J.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 39:12(2019), pp. 7031-7056. [10.3934/dcds.2019243]
The area blow up set for bounded mean curvature submanifolds with respect to elliptic surface energy functionals
De Philippis, G.;
2019-01-01
Abstract
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 [12], 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 [10].I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
