标量曲率有下界的自旋填充的刚性
Rigidity for spin fill-ins with scalar curvature bounded from below
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中文总结 AI 辅助
针对标量曲率有下界的紧致自旋填充，证明Brendle等人的超球半径不等式取等时，该流形等距于双曲空间中的测地球，建立了该等号情形的刚性结论。
中文摘要 AI 辅助
我们建立了Brendle、Tsiamis和Wang提出的超球半径不等式在等号成立时的刚性结论，该结论针对标量曲率有下界的紧致自旋填充。更确切地说，设$(M^{n\geq 3},g)$是紧致连通黎曼自旋流形，具有连通边界$\u03a3$且标量曲率满足$\u0394_g\geq -n(n-1)$。我们证明，当Brendle、Tsiamis和Wang给出的上界$\inf_{\u03a3}H\leq (n-1)\sqrt{1+\operatorname{Rad}(\u03a3)^{-2}}$取等时，$(M,g)$等距于双曲空间中的测地球。
英文摘要
We establish the rigidity statement in the equality case of the hyperspherical-radius inequality of Brendle, Tsiamis, and Wang for compact spin fill-ins with scalar curvature bounded below. More precisely, let $(M^{n\geq 3},g)$ be a compact, connected Riemannian spin manifold having a connected boundary $Σ$ and scalar curvature satisfying $\mathrm{scal}_g\geq -n(n-1)$. We prove that equality in the upper bound \[ \inf_ΣH\leq (n-1)\sqrt{1+\operatorname{Rad}(Σ)^{-2}} \] given by Brendle, Tsiamis, and Wang holds if and only if $(M,g)$ is isometric to a geodesic ball in hyperbolic space.
