Quadratic tilt-excess decay and strong maximum principle for varifolds

Schätzle, Reiner¹

¹ Mathematisches Institut Rheinischen Friedrich-Wilhelms-Universität Bonn Beringstraße 6, D-53115 Bonn, Germany

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 1, pp. 171-231

Résumé

In this paper, we prove that integral $n$-varifolds $\mu$ in codimension 1 with $H_{\mu }\in L_{\mathrm{loc}}^p\left(\mu \right)$, $p>n$, $p\ge 2$ have quadratic tilt-excess decay ${\mathrm{tiltex}}_{\mu }(x,\varrho ,T_x\mu )=O_x\left({\varrho }^2\right)$for $\mu$-almost all $x$, and a strong maximum principle which states that these varifolds cannot be touched by smooth manifolds whose mean curvature is given by the weak mean curvature $H_{\mu }$, unless the smooth manifold is locally contained in the support of $\mu$.

Détail

Classification : 49Q15, 35J60, 53A10