Minkowski Inequality in Cartan–Hadamard Manifolds.
- Resource Type
- Article
- Authors
- Ghomi, Mohammad; Spruck, Joel
- Source
- IMRN: International Mathematics Research Notices. Oct2023, Vol. 2023 Issue 20, p17892-17910. 19p.
- Subject
- *ISOPERIMETRIC inequalities
*CONVEX surfaces
*CONVEX functions
*CURVATURE
*SURFACE area
- Language
- ISSN
- 1073-7928
Using harmonic mean curvature flow, we establish a sharp Minkowski-type lower bound for total mean curvature of convex surfaces with a given area in Cartan-Hadamard |$3$| -manifolds. This inequality also improves the known estimates for total mean curvature in hyperbolic |$3$| -space. As an application, we obtain a Bonnesen-style isoperimetric inequality for surfaces with convex distance function in nonpositively curved |$3$| -spaces, via monotonicity results for total mean curvature. This connection between the Minkowski and isoperimetric inequalities is extended to Cartan–Hadamard manifolds of any dimension. [ABSTRACT FROM AUTHOR]