Rigidity for critical metrics of the volume functional
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DOI: 10.1002/mana.201700240
Abstract: Geodesic balls in a simply connected space forms $\mathbb{S}^n$, $\mathbb{R}^{n}$ or $\mathbb{H}^{n}$ are distinguished manifolds for comparison in bounded Riemannian geometry. In this paper we show that they have the maximum possible boundary volume among… read more here.
Keywords: volume; volume functional; critical metrics; rigidity critical ... See more keywords
Isoperimetric inequality and Weitzenböck type formula for critical metrics of the volume
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DOI: 10.1007/s11856-019-1930-2
Abstract: We provide an isoperimetric inequality for critical metrics of the volume functional with nonnegative scalar curvature on compact manifolds with boundary. In addition, we establish a Weitzenb\"ock type formula for critical metrics of the volume… read more here.
Keywords: critical metrics; isoperimetric inequality; metrics volume; type formula ... See more keywords
Kähler–Einstein metrics and volume minimization
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DOI: 10.1016/j.aim.2018.10.038
Abstract: We prove that if a $\mathbb{Q}$-Fano variety $V$ specially degenerates to a K\"{a}hler-Einstein $\mathbb{Q}$-Fano variety $V$, then for any ample Cartier divisor $H=-r^{-1} K_V$ with $r\in \mathbb{Q}_{>0}$, the normalized volume $\widehat{\rm vol}(v)=A_{\mathcal{C}}^n(v)\cdot {\rm vol}(v)$ is… read more here.
Keywords: einstein metrics; hler einstein; einstein; metrics volume ... See more keywords