Author:
Agostiniani Virginia, ,Mazzieri Lorenzo,Oronzio Francesca, ,
Abstract
<abstract><p>In this paper, we prove that associated with a sub-static asymptotically flat manifold endowed with a harmonic potential there is a one-parameter family $ \{F_{\beta}\} $ of functions which are monotone along the level-set flow of the potential. Such monotonicity holds up to the optimal threshold $ \beta = \frac{n-2}{n-1} $ and allows us to prove a geometric capacitary inequality where the capacity of the horizon plays the same role as the ADM mass in the celebrated Riemannian Penrose Inequality.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Mathematical Physics,Analysis
Reference27 articles.
1. V. Agostiniani, M. Fogagnolo, L. Mazzieri, Minkowski inequalities via nonlinear potential theory, 2020, arXiv: 1906.00322.
2. V. Agostiniani, L. Mazzieri, On the geometry of the level sets of bounded static potentials, Commun. Math. Phys., 355 (2017), 261–301.
3. V. Agostiniani, L. Mazzieri, Monotonicity formulas in potential theory, Calc. Var., 59 (2020), 1–32.
4. R. Bartnik, The mass of an asymptotically flat manifold, Commun. Pure Appl. Math., 39 (1986), 661–693.
5. L. Benatti, M. Fogagnolo, L. Mazzieri, Minkowski inequality on complete Riemannian manifolds with nonnegative Ricci curvature, 2021, arXiv: 2101.06063v4.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献