Quadratic tilt-excess decay and strong maximum principle for varifolds
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 3 (2004) no. 1, p. 171-231

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 ${\mathrm{tiltex}}_{\mu }\left(x,\varrho ,{T}_{x}\mu \right)={O}_{x}\left({\varrho }^{2}\right)$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 $\mu$.

Classification:  49Q15,  35J60,  53A10
@article{ASNSP_2004_5_3_1_171_0,
author = {Sch\"atzle, Reiner},
title = {Quadratic tilt-excess decay and strong maximum principle for varifolds},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 3},
number = {1},
year = {2004},
pages = {171-231},
zbl = {1096.49023},
mrnumber = {2064971},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2004_5_3_1_171_0}
}

Schätzle, Reiner. Quadratic tilt-excess decay and strong maximum principle for varifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 3 (2004) no. 1, pp. 171-231. http://www.numdam.org/item/ASNSP_2004_5_3_1_171_0/

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