https://neckpinch.com/authors/giulio-colombo/New arXiv papers by Giulio Colombo, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2007.07194/arxiv:2007.07194Tue, 14 Jul 2020 00:00:00 GMTBruno Bianchini, Giulio Colombo, Marco Magliaro, Luciano Mari, Patrizia Pucci, Marco Rigoli — This survey describes some recent rigidity results obtained by the authors for the prescribed mean curvature problem on graphs u : M → ℝ. Emphasis is put on minimal, CMC and capillary graphs, as well as on graphical solitons for the mean curvature flow, in warped product ambient spaces. A detailed analysis of the mean curvature operator is given, focusing on maximum principles at infinity, Liouville properties, gradient estimates. Among the geometric applications, we mention the Bernstein theorem for positive entire minimal graphs on manifolds with non-negative Ricci curvature, and a splitting theorem for capillary graphs over an unbounded domain Ω⊂ M, namely, for CMC graphs satisfying an overdetermined boundary condition.Mean curvature flowStability & uniquenessBoundaries & non-compactFree boundary & capillaryRotational symmetry & warped productsDiscrete & graph Ricci https://neckpinch.com/papers/1811.10968/arxiv:1811.10968Tue, 27 Nov 2018 00:00:00 GMTGiulio Colombo, Luciano Mari, Marco Rigoli — 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 flowStability & uniquenessRotational symmetry & warped products