Minkowski inequalities via nonlinear potential theory
V Agostiniani, M Fogagnolo, L Mazzieri - Archive for Rational Mechanics …, 2022 - Springer
In this paper, we prove an extended version of the Minkowski Inequality, holding for any
smooth bounded set Ω⊂ R n, n≥ 3. Our proof relies on the discovery of effective …
smooth bounded set Ω⊂ R n, n≥ 3. Our proof relies on the discovery of effective …
A Minkowski-type inequality for capillary hypersurfaces in a half-space
In this article, we investigate a flow of inverse mean curvature type for capillary
hypersurfaces in the half-space. We establish the global existence of solutions for this flow …
hypersurfaces in the half-space. We establish the global existence of solutions for this flow …
Minkowski inequality on complete Riemannian manifolds with nonnegative Ricci curvature
In this paper we consider Riemannian manifolds of dimension at least $3 $, with
nonnegative Ricci curvature and Euclidean Volume Growth. For every open bounded subset …
nonnegative Ricci curvature and Euclidean Volume Growth. For every open bounded subset …
Comparison geometry for substatic manifolds and a weighted Isoperimetric Inequality
S Borghini, M Fogagnolo - arXiv preprint arXiv:2307.14618, 2023 - arxiv.org
Substatic Riemannian manifolds with minimal boundary arise naturally in General Relativity
as spatial slices of static spacetimes satisfying the Null Energy Condition. Moreover, they …
as spatial slices of static spacetimes satisfying the Null Energy Condition. Moreover, they …
A rigidity theorem for asymptotically flat static manifolds and its applications
In this paper, we study the Minkowski-type inequality for asymptotically flat static manifolds
$(M^{n}, g) $ with boundary and with dimension $ n< 8$ that was established by McCormick …
$(M^{n}, g) $ with boundary and with dimension $ n< 8$ that was established by McCormick …
On a Minkowski-like inequality for asymptotically flat static manifolds
S McCormick - Proceedings of the American Mathematical Society, 2018 - ams.org
The Minkowski inequality is a classical inequality in differential geometry giving a bound
from below on the total mean curvature of a convex surface in Euclidean space, in terms of …
from below on the total mean curvature of a convex surface in Euclidean space, in terms of …
[HTML][HTML] Minkowski inequality for nearly spherical domains
F Glaudo - Advances in Mathematics, 2022 - Elsevier
We investigate the validity and the stability of various Minkowski-like inequalities for C 1-
perturbations of the ball. Let K⊆ R n be a domain (possibly not convex and not mean …
perturbations of the ball. Let K⊆ R n be a domain (possibly not convex and not mean …
On weak inverse mean curvature flow and Minkowski-type inequalities in hyperbolic space
B Harvie - arXiv preprint arXiv:2404.08410, 2024 - arxiv.org
We prove that a proper weak solution $\{\Omega_ {t}\} _ {0\leq t<\infty} $ to inverse mean
curvature flow in $\mathbb {H}^{n} $, $3\leq n\leq 7$, is smooth and star-shaped by the …
curvature flow in $\mathbb {H}^{n} $, $3\leq n\leq 7$, is smooth and star-shaped by the …
The Minkowski inequality in de Sitter space
J Scheuer - Pacific Journal of Mathematics, 2021 - msp.org
The classical Minkowski inequality in the Euclidean space provides a lower bound on the
total mean curvature of a hypersurface in terms of the surface area, which is optimal on …
total mean curvature of a hypersurface in terms of the surface area, which is optimal on …
Quasi-spherical metrics and the static Minkowski inequality
B Harvie, YK Wang - arXiv preprint arXiv:2403.06216, 2024 - arxiv.org
We prove that equality within the Minkowski inequality for asymptotically flat static spaces is
achieved only by slices in Schwarzschild space for mean-convex, non-negative scalar …
achieved only by slices in Schwarzschild space for mean-convex, non-negative scalar …