This thesis is dedicated to the interior and boundary regularity of the mean curvature flow. We prove that, if a mean curvature flow with boundary and transport term is close enough to a stationary half-plane with density one, then it is $C^{1,\alpha}$. Our approach exploits the maximum principle for the mean curvature flow and Huisken's monotonicity formula. With the same techniques, we also provide a self-contained proof of Allard's regularity theorem.

Epsilon-regularity for the mean curvature flow with boundary and transport term: a viscosity approach / Gasparetto, Carlo. - (2022 Dec 20).

### Epsilon-regularity for the mean curvature flow with boundary and transport term: a viscosity approach

#### Abstract

This thesis is dedicated to the interior and boundary regularity of the mean curvature flow. We prove that, if a mean curvature flow with boundary and transport term is close enough to a stationary half-plane with density one, then it is $C^{1,\alpha}$. Our approach exploits the maximum principle for the mean curvature flow and Huisken's monotonicity formula. With the same techniques, we also provide a self-contained proof of Allard's regularity theorem.
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De Philippis, Guido
Gasparetto, Carlo
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Descrizione: tesi di Ph.D.
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