Remarks on mean curvature flow solitons in warped products

Giulio Colombo, ,Dipartimento di Matematica, Università degli Studi di Milano, via Cesare Saldini, 50, Milano, 20133, Italy, Luciano Mari, Marco Rigoli, ,Scuola Normale Superiore, Piazza dei Cavalieri, 7, Pisa, 56124, Italy, ,Dipartimento di Matematica, Università degli Studi di Milano, via Cesare Saldini, 50, Milano, 20133, Italy
2018 Discrete and Continuous Dynamical Systems. Series S  
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.
doi:10.3934/dcdss.2020153 fatcat:wc4tbkhwqjgk3ho5vbblakkisq