双倍Schwarzschild 3-流形中有限拓扑的完备极小曲面

Isoperimetric and Weingarten surfaces in the Schwarzschild manifold

We show that any star-shaped convex hypersurface with constant Weingarten curvature in the deSitter-Schwarzschild manifold is a sphere of symmetry. Moreover, we study an isoperimetric problem for bounded domains in the doubled Schwarzschild manifold. We prove the existence of an isoperimetric surface for any value of the enclosed volume, and we completely describe the isoperimetric surfaces for very large enclosed volume. This complements work in H. Bray's thesis, where isoperimetric surfaces homologous to the horizon are studied.

The area preserving Willmore flow and local maximizers of the Hawking mass in asymptotically Schwarzschild manifolds

We study the area preserving Willmore flow in an asymptotic region of an asymptotically flat manifold which is $C^{3}-$close to Schwarzschild. It was shown by Lamm, Metzger and Schulze that such an end is foliated by spheres of Willmore type. In this paper, we prove that the leaves of this foliation are stable under small area preserving $W^{2,2}-$perturbations with respect to the area preserving Willmore flow. This implies, in particular, that the leaves are strict local area preserving maximizers of the Hawking mass with respect to the $W^{2,2}-$topology.

A QP perspective on topology change in Poisson-Lie T-duality

We describe topological T-duality and Poisson-Lie T-duality in terms of QP (differential graded symplectic) manifolds and their canonical transformations. Duality is mediated by a QP-manifold on doubled non-abelian "correspondence" space, from which we can perform mutually dual symplectic reductions, where certain canonical transformations play a vital role. In the presence of spectator coordinates, we show how the introduction of "bibundle" structure on correspondence space realises changes in the global fibration structure under Poisson-Lie duality. Our approach can be directly translated to…

三维黎曼Penrose不等式稳定性

Stability for the 3D Riemannian Penrose inequality

研究证明Schwarzschild 3流形在特定拓扑下满足三维黎曼Penrose不等式的稳定性条件。

具有秩一非阿贝尔对称性的正曲率六维流形的轨道分层与光滑拓扑

Orbit stratifications and smooth topology of positively curved six-manifolds with rank-one nonabelian symmetry

本文研究带SO(3)或SU(2)有效等距作用的正曲率六维流形，细化轨道分层并完成多类商空间的光滑拓扑分类，建立相关曲率障碍，部分结果由ChatGPT-6-astra发现并验证。

任意拓扑中带电静电黑洞的存在性

On the existence of charged electrostatic black holes in arbitrary topology

本文研究任意拓扑下S1对称静态电真空黑洞的存在性，证明除Schwarzschild外，Boost与Myers-Korotkin-Nicolai真空黑洞无法带电并保持渐近行为，揭示3+1维中电荷、拓扑与渐近性的复杂关系。