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Liouville theorem on p-biharmonic map from gradient Ricci soliton

Xiangzhi Cao

Abstract

In this paper, we are devoted to obtain some results on p-biharmonic map from gradient Ricci soliton, especially on two dimensional cigar soliton.

Liouville theorem on p-biharmonic map from gradient Ricci soliton

Abstract

In this paper, we are devoted to obtain some results on p-biharmonic map from gradient Ricci soliton, especially on two dimensional cigar soliton.
Paper Structure (5 sections, 15 theorems, 56 equations)

This paper contains 5 sections, 15 theorems, 56 equations.

Table of Contents

  1. Introduction
  2. $B$-$L$-map and $p$-$q$-biharmonic map
  3. The first variation formula
  4. $p$-$q$-biharmonic map
  5. $p$-biharmonic map

Key Result

Lemma 1

Assume that $(M,g,f)$ is a gradient Ricci soliton. Then the following equation holds for some constant C.

Theorems & Definitions (22)

  • Lemma 1: cf.MR2448435
  • Lemma 2: cf. MR2448435
  • Theorem 1.1
  • Theorem 1.2
  • Theorem 2.1
  • proof
  • Theorem 2.2
  • Theorem 2.3
  • Lemma 3: cf.zbMATH06268870
  • Lemma 4: cf.zbMATH06268870
  • ...and 12 more