TY - JOUR
T1 - On the mean curvature type flow for convex capillary hypersurfaces in the ball
AU - Hu, Yingxiang
AU - Wei, Yong
AU - Yang, Bo
AU - Zhou, Tailong
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2023/9
Y1 - 2023/9
N2 - In this paper, we study the mean curvature type flow for hypersurfaces in the unit Euclidean ball with capillary boundary, which was introduced by Wang and Xia (Commun Anal Geom, 2019) and Wang and Weng (Calc Var Partial Differ Equ 59(5):149–174, 2020). We show that if the initial hypersurface is strictly convex, then the solution of this flow is strictly convex for t> 0 , exists for all positive time and converges smoothly to a spherical cap. As an application, we prove a family of new Alexandrov–Fenchel inequalities for convex hypersurfaces in the unit Euclidean ball with capillary boundary.
AB - In this paper, we study the mean curvature type flow for hypersurfaces in the unit Euclidean ball with capillary boundary, which was introduced by Wang and Xia (Commun Anal Geom, 2019) and Wang and Weng (Calc Var Partial Differ Equ 59(5):149–174, 2020). We show that if the initial hypersurface is strictly convex, then the solution of this flow is strictly convex for t> 0 , exists for all positive time and converges smoothly to a spherical cap. As an application, we prove a family of new Alexandrov–Fenchel inequalities for convex hypersurfaces in the unit Euclidean ball with capillary boundary.
UR - https://www.scopus.com/pages/publications/85168357157
U2 - 10.1007/s00526-023-02554-y
DO - 10.1007/s00526-023-02554-y
M3 - 文章
AN - SCOPUS:85168357157
SN - 0944-2669
VL - 62
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 7
M1 - 209
ER -