activity
20232026
collaborators

8 papers

math.DG2026

Scalar Curvature Compactness for Warped Products on with Varying Base Metrics

Changliang Wang, Zhixin Wang

We study the Gromov--Sormani MinA scalar curvature compactness conjecture for warped product metrics on of the form introduced by Kazaras-Xu in \ci…

math.DG2025

Singular metrics with nonnegative scalar curvature and RCD

Xianzhe Dai, Changliang Wang, Lihe Wang +1

We show that a uniformly Euclidean metric with isolated singularity on , where or , spin, and nonnegative scalar curvature on the s…

math.DG2025

Gap phenomenon for scalar curvature

Yukai Sun, Changliang Wang

Inspired by Goette-Semmelmann \cite{GSSU2002}, we derive an estimate for the scalar curvature without a nonnegativity assumption on curvature operator. As an application, we show t…

math.DG2024

Positive scalar curvature and isolated conical singularity

Xianzhe Dai, Yukai Sun, Changliang Wang

We prove a Geroch type result for isolated conical singularity. Namely, we show that there is no Riemannian metric on with an isolated conical singularity which ha…

math.DG2024

On the Scalar Curvature Compactness Conjecture in the Conformal Case

Brian Allen, Wenchuan Tian, Changliang Wang

Is a sequence of Riemannian manifolds with positive scalar curvature, satisfying some conditions to keep the sequence reasonable, compact? What topology should one use for the conv…

math.DG2024

Oberwolfach Workshop Report: Analysis, Geometry and Topology of Positive Scalar Curvature Metrcs: Limits of sequences of manifolds with nonnegative scalar curvature and other hypotheses

Christina Sormani wth Wenchuan Tian, Changliang Wang

This report contains a survey of examples of sequences of manifolds with nonnegative scalar curvature including an extreme example with Wenchuan Tian and Changliang Wang. It announ…

math.DG2024

Positive mass theorem for asymptotically flat manifolds with isolated conical singularities

Xianzhe Dai, Yukai Sun, Changliang Wang

We prove the positive mass theorem for asymptotical flat (AF for short) manifolds with finitely many isolated conical singularities. We do not impose the spin condition. Instead we…

math.DG2023

Positive mass theorem for asymptotically flat spin manifolds with isolated conical singularities

Xianzhe Dai, Yukai Sun, Changliang Wang

There has been a lot of interests in Positive Mass Theorems for singular metrics on smooth manifolds. We prove a positive mass theorem for asymptotically flat (AF) spin manifolds w…