Sharp upper bounds of p-capacity in convex cone and asymptotically flat half-space
摘要
In this paper, we prove some sharp upper bounds for p-capacity inequalities of star-shaped hypersurfaces with free boundary in convex cones by inverse mean curvature flow with Neumann boundary condition. As a second result, we establish a sharp upper bound for the p-capacity of the surface and mass-p-capacity inequality in 3-dimensional asymptotically flat half-space which generalized Silva’s results (Lett Math Phys 115(2): 19 pp, 2025), by using weak inverse mean curvature flow for surfaces with free boundary.