论文标题
在等级里曼尼亚人的不平等现象上
On the Isoperimetric Riemannian Penrose Inequality
论文作者
论文摘要
我们证明，Riemannian Penrose不平等的不平等范围为$ 3 $ 3 $ - 具有非负标量曲率和连接的地平线边界（只要满足最佳衰减假设），这会导致$ \ MATHRM {ADM} $质量质量明确。我们的证明是建立在霍金质量和IT潜在理论版本之间的新颖相互作用的基础上，该版本最近由Agostiniani，Oronzio和第三名命名作者引入。结果，我们在上述敏锐的假设下建立了$ \ mathrm {adm} $质量和Huisken的等值质量之间的平等。此外，我们在任何$ 3 $ manifold上具有非负标量曲率，连接的地平线边界的等值质量的质量，建立了riemannian penrose不平等，并支持较弱的逆平均曲率流量。特别是，这种等法riemannian penrose不平等不需要歧管的渐近平坦度。该论点是基于涉及Huisken等等质量质量和鹰质量的新的渐近比较结果。
We prove that the Riemannian Penrose Inequality holds for Asymptotically Flat $3$-manifolds with nonnegative scalar curvature and connected horizon boundary, provided the optimal decay assumptions are met, which result in the $\mathrm{ADM}$ mass being a well-defined geometric invariant. Our proof builds on a novel interplay between the Hawking mass and a potential-theoretic version of it, recently introduced by Agostiniani, Oronzio and the third named author. As a consequence, we establish the equality between $\mathrm{ADM}$ mass and Huisken's Isoperimetric mass under the above sharp assumptions. Moreover, we establish a Riemannian Penrose Inequality in terms of the Isoperimetric mass on any $3$-manifold with nonnegative scalar curvature, connected horizon boundary, and which supports a well-posed notion of weak Inverse Mean Curvature Flow. In particular, such Isoperimetric Riemannian Penrose Inequality does not require the asymptotic flatness of the manifold. The argument is based on a new asymptotic comparison result involving Huisken's Isoperimetric mass and the Hawking mass.
