Some recent advances in nonlinear diffusion on negatively-curved Riemannian manifolds: from barriers to smoothing effects

Bollettino dell'Unione Matematica Italiana volume 14, pages69–97(2021)Cite this article

Abstract

In this survey paper we discuss a series of recent results concerning nonnegative solutions to nonlinear diffusion equations of porous-medium type on Cartan–Hadamard manifolds, a special class of negatively-curved Riemannian manifolds that generalize the Euclidean space. We focus on sharp barrier estimates, asymptotic convergence and smoothing effects, describing quantitatively how the curvature behavior at infinity affects the way solutions depart from having a Euclidean-like structure.

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  1. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy

    Matteo Muratori

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  1. Matteo Muratori
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Muratori, M. Some recent advances in nonlinear diffusion on negatively-curved Riemannian manifolds: from barriers to smoothing effects. Boll Unione Mat Ital 14, 69–97 (2021). https://doi.org/10.1007/s40574-020-00238-5

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