The aim of this paper is to prove some classification results for generic shrinking Ricci solitons. In particular, we show that every three– dimensional generic shrinking Ricci soliton is given by quotients of either 𝕊3, ℝ×𝕊2 or ℝ3 under some very weak conditions on the vector field X generating the soliton structure. In doing so we introduce analytical tools that could be useful in other settings; for instance we prove that the Omori-Yau maximum principle holds for the X-Laplacian on every generic Ricci soliton without any assumption on X.

Analytic and geometric properties of generic Ricci solitons / C. G., P. Mastrolia, M. D. D., M. Rigoli. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 368:11(2016 Nov), pp. 7533-7549. [10.1090/tran/6864]

Analytic and geometric properties of generic Ricci solitons

P. Mastrolia
Secondo
;
M. Rigoli
Ultimo
2016

Abstract

The aim of this paper is to prove some classification results for generic shrinking Ricci solitons. In particular, we show that every three– dimensional generic shrinking Ricci soliton is given by quotients of either 𝕊3, ℝ×𝕊2 or ℝ3 under some very weak conditions on the vector field X generating the soliton structure. In doing so we introduce analytical tools that could be useful in other settings; for instance we prove that the Omori-Yau maximum principle holds for the X-Laplacian on every generic Ricci soliton without any assumption on X.
Omori-Yau maximum principle; Ricci solitons; rigidity results; mathematics (all); applied mathematics
Settore MAT/03 - Geometria
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/449489
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