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

Gasparetto, Carlo
2022-12-20

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.
De Philippis, Guido
Gasparetto, Carlo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/130591
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