From the 1 of 43 linked papers with an AI index.
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Volume Stability for Hyperbolic Manifolds and Applications to General Relativity
Puskar Mondal, Shing-Tung Yau
The paper proves that for closed hyperbolic 3‑manifolds, any sequence of metrics with scalar curvature ≥ −6 whose volumes approach the hyperbolic volume must converge in the C⁰ sen…
The Critical LYZ Equation in Kähler Geometry
Jixiang Fu, Shing-Tung Yau, Dekai Zhang
We establish the existence of smooth solutions for the LYZ equation at the critical phase , thereby solving the critical case of a problem posed by Collins-Jaco…
Ollivier Ricci-flow on weighted graphs
Shuliang Bai, Yong Lin, Linyuan Lu +2
We study the existence of solutions of Ricci flow equations of Ollivier-Lin-Lu-Yau curvature defined on weighted graphs. Our work is motivated by\cite{NLLG} in which the discrete t…
A new flow solving the LYZ equation in Kähler geometry
Jixiang Fu, Shing-Tung Yau, Dekai Zhang
We introduced a new flow to the LYZ equation on a compact Kähler manifold. We first show the existence of the longtime solution of the flow. We then show that under the Collins-Ja…