A Minkowski inequality for Horowitz-Myers geon

Metrics of Horowitz-Myers type with the negative constant scalar curvature

We construct a one-parameter family of complete metrics of Horowitz-Myers type with the negative constant scalar curvature. We also verify a positive energy conjecture of Horowitz-Myers for these metrics.

Horowitz-Myers猜想中的刚性陈述

The rigidity statement in the Horowitz-Myers conjecture

本文通过另一种方法证明了Horowitz-Myers猜想在特定维度下的成立，并展示了达到等式的度量与Horowitz-Myers度量的局部等距关系。

收缩不等式与Horowitz-Myers猜想

Systolic inequalities and the Horowitz-Myers conjecture

对于3至7维紧流形，在标量曲率下界条件下，建立了边界平均曲率下确界与边界收缩之间的关系，并由此得到新的正能量定理，等号由Horowitz-Myers度规实现。

The rigid Horowitz-Myers conjecture

The "new positive energy conjecture" Horowitz and Myers (1999) probes a possible nonsupersymmetric AdS/CFT correspondence. We consider a version formulated for complete, asymptotically Poincaré-Einstein Riemannian metrics $(M,g)$ with bounded scalar curvature $R\ge -n(n-1)$. This version then asserts that any such $(M,g)$ must have mass not less than the mass $m_0$ of a metric $g_0$ induced on a time-symmetric slice of a certain AdS soliton spacetime. The conjecture remains unproved, having so far resisted standard techniques. Little is known other than that the conjecture is true for metrics …