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Positive mass theorem on conical manifold with small cone angle

Yaoting Gui

Abstract

We prove the positive mass theorem on conical manifold with small cone angle and co-dimensional two singularities under the assumption that the ambient manifold admits a spin structure and locally conformal flat

Positive mass theorem on conical manifold with small cone angle

Abstract

We prove the positive mass theorem on conical manifold with small cone angle and co-dimensional two singularities under the assumption that the ambient manifold admits a spin structure and locally conformal flat
Paper Structure (3 sections, 2 theorems, 38 equations)

This paper contains 3 sections, 2 theorems, 38 equations.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Proof of the Positive mass

Key Result

Theorem 1.1

Let $M$ be a conical manifold with a singular set $X$ of codimension 2 and $\beta\in(-1,0)$. Suppose the ambient manifold is spin and locally conformal flat with positive Yamabe constant, then the mass of $M$ is non-negative. More precisely, let $q\in M\setminus X$ be a regular point. Consider the c

Theorems & Definitions (14)

  • Theorem 1.1: Positive Mass Theorem
  • Remark 1.2
  • Remark 1.3
  • Remark 1.4
  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Remark 2.4
  • Remark 2.5
  • Proposition 3.1
  • ...and 4 more