In this paper, we introduce a volume- or area-preserving curvature flow for hypersurfaces with capillary boundary in the half-space, with speed given by a positive power of the mean curvature with a non-local averaging term. We demonstrate that for any convex initial hyper- surface with a capillary boundary, the flow exists for all time and smoothly converges to a spherical cap as t → +∞.
Sinestrari, C., Weng, L. (2024). Hypersurfaces with capillary boundary evolving by volume preserving power mean curvature flow. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 63(9) [10.1007/s00526-024-02838-x].
Hypersurfaces with capillary boundary evolving by volume preserving power mean curvature flow
Carlo Sinestrari
;Liangjun Weng
2024-01-01
Abstract
In this paper, we introduce a volume- or area-preserving curvature flow for hypersurfaces with capillary boundary in the half-space, with speed given by a positive power of the mean curvature with a non-local averaging term. We demonstrate that for any convex initial hyper- surface with a capillary boundary, the flow exists for all time and smoothly converges to a spherical cap as t → +∞.File in questo prodotto:
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