We study some properties of mean curvature flow solitons in general Riemannian manifolds and in warped products, with emphasis on constant curvature and Schwarzschild type spaces. We focus on splitting and rigidity results under various geometric conditions, ranging from the stability of the soliton to the fact that the image of its Gauss map be contained in suitable regions of the sphere. We also investigate the case of entire graphs.

Remarks on mean curvature flow solitons in warped products / G. Colombo, L. Mari, M. Rigoli. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 13:7(2020 Jul), pp. 1957-1991. [10.3934/dcdss.2020153]

Remarks on mean curvature flow solitons in warped products

G. Colombo
Primo
;
L. Mari
Secondo
;
M. Rigoli
Ultimo
2020-07

Abstract

We study some properties of mean curvature flow solitons in general Riemannian manifolds and in warped products, with emphasis on constant curvature and Schwarzschild type spaces. We focus on splitting and rigidity results under various geometric conditions, ranging from the stability of the soliton to the fact that the image of its Gauss map be contained in suitable regions of the sphere. We also investigate the case of entire graphs.
Mean curvature flow; Self-shrinker; Soliton; Splitting theorem; Warped product;
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: http://hdl.handle.net/2434/802386
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