https://neckpinch.com/authors/matheus-nunes-soares/New arXiv papers by Matheus Nunes Soares, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2603.12548/arxiv:2603.12548Fri, 13 Mar 2026 00:00:00 GMTClaudia Fernandes, Jorge de Lira, Matheus Soares — A priori estimates for the mean curvature evolution of Killing graphs in Cartan-Hadamard manifolds with asymptotic Dirichlet conditions are established. As an application, the existence of the corresponding parabolic flow is proved, ensuring regularity of the obtained solutions through the construction of suitable barriers at points of the asymptotic boundary. Such a construction is made possible under an appropriate notion of convexity at infinity.Mean curvature flow https://neckpinch.com/papers/2602.11930/arxiv:2602.11930Thu, 12 Feb 2026 00:00:00 GMTJocel Faustino Norberto de Oliveira, Jorge Herbert Soares de Lira, Matheus Nunes Soares — We obtain height, gradient, and curvature a priori estimates for a modified mean curvature flow in Riemannian manifolds endowed with a Killing vector field. As a consequence, we prove the existence of smooth, entire, longtime solutions for this extrinsic flow with smooth initial data.Mean curvature flowLong-time existence & convergence