The second variation of the Ricci expander entropy

Meng Zhu

doi:10.2140/pjm.2011.251.499

The second variation of the Ricci expander entropy

Meng Zhu^*

^*Corresponding author for this work

Lehigh University

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

The critical points of theW₊ functional introduced by M. Feldman, T. Ilmanen and L. Ni are the expanding Ricci solitons, which are special solutions of the Ricci flow. On compact manifolds, expanding solitons coincide with Einstein metrics. In this paper, we compute the first and second variations of the entropy functional of theW₊ functional, and briefly discuss the linear stability of compact hyperbolic space forms.

Original language	English
Pages (from-to)	499-510
Number of pages	12
Journal	Pacific Journal of Mathematics
Volume	251
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2011.251.499
State	Published - 2011
Externally published	Yes

Keywords

Entropy functional
Linear stability
Linear variation
Negative einstein manifold
Second variation
W functional
ν functional

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10.2140/pjm.2011.251.499

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abstract = "The critical points of theW+ functional introduced by M. Feldman, T. Ilmanen and L. Ni are the expanding Ricci solitons, which are special solutions of the Ricci flow. On compact manifolds, expanding solitons coincide with Einstein metrics. In this paper, we compute the first and second variations of the entropy functional of theW+ functional, and briefly discuss the linear stability of compact hyperbolic space forms.",

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AB - The critical points of theW+ functional introduced by M. Feldman, T. Ilmanen and L. Ni are the expanding Ricci solitons, which are special solutions of the Ricci flow. On compact manifolds, expanding solitons coincide with Einstein metrics. In this paper, we compute the first and second variations of the entropy functional of theW+ functional, and briefly discuss the linear stability of compact hyperbolic space forms.

KW - Entropy functional

KW - Linear stability

KW - Linear variation

KW - Negative einstein manifold

KW - Second variation

KW - W functional

KW - ν functional

UR - https://www.scopus.com/pages/publications/79959208455

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DO - 10.2140/pjm.2011.251.499

M3 - 文章

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SN - 0030-8730

VL - 251

SP - 499

EP - 510

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -

The second variation of the Ricci expander entropy

Abstract

Keywords

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