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A Schur's type volume comparison theorem

Xiaole Su, Yi Tan, Yusheng Wang

Abstract

In this paper, inspired by Schur's comparison theorem about curves in Euclidean space, we mainly provide a Schur's type volume comparison theorem, which is about the volumes of the boundaries of open balls in a complete $n$-dimensional Riemannian manifold with Ricci$\geq (n-1)k$.

A Schur's type volume comparison theorem

Abstract

In this paper, inspired by Schur's comparison theorem about curves in Euclidean space, we mainly provide a Schur's type volume comparison theorem, which is about the volumes of the boundaries of open balls in a complete -dimensional Riemannian manifold with Ricci.
Paper Structure (4 sections, 57 equations)

This paper contains 4 sections, 57 equations.

Table of Contents

  1. Main results
  2. Two lemmas on real functions
  3. Proofs of Theorems A and C
  4. An application of Lemma 2.2

Theorems & Definitions (8)

  • proof
  • proof
  • proof : Proof of Lemma 2.2
  • proof
  • proof
  • proof
  • proof : Proof of Theorem A
  • proof : Proof of Theorem C