Remarks on mean curvature flow solitons in warped products

Giulio Colombo; Luciano Mari; Marco Rigoli

doi:10.3934/dcdss.2020153

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2020, Volume 13, Issue 7: 1957-1991. Doi: 10.3934/dcdss.2020153

This issue Previous Article Existence theorems for generalized nonlinear quadratic integral equations via a new fixed point result Next Article Schrödinger–Kirchhoff–Hardy

$ p $

–fractional equations without the Ambrosetti–Rabinowitz condition

Remarks on mean curvature flow solitons in warped products

1.
Dipartimento di Matematica, Università degli Studi di Milano, via Cesare Saldini, 50, Milano, 20133, Italy
2.
Scuola Normale Superiore, Piazza dei Cavalieri, 7, Pisa, 56124, Italy
3.
Dipartimento di Matematica, Università degli Studi di Milano, via Cesare Saldini, 50, Milano, 20133, Italy

^* Corresponding author
^* Corresponding author

Dedicated to Patrizia Pucci on her 65^th birthday

Received: April 30, 2018

Revised: November 30, 2018

Published: April 2020

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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.

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Mathematics Subject Classification: Primary: 53C44, 53C42, 53C40; Secondary: 35B50, 35B06.

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