https://neckpinch.com/authors/marcus-antonio-mendonca-marrocos/New arXiv papers by Marcus Antônio Mendonça Marrocos, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2603.26903arxiv:2603.26903Fri, 27 Mar 2026 00:00:00 GMTJosé Nazareno Vieira Gomes, Marcus Antonio Mendonça Marrocos — We develop a method for constructing complete gradient Ricci solitons realized as fiber bundles endowed with warped metrics, and we establish necessary and sufficient conditions for their existence. As an application, we present new examples of complete gradient steady and shrinking Ricci solitons obtained via quotients by isometric group actionsRicci solitons https://arxiv.org/abs/2306.06504arxiv:2306.06504Sat, 10 Jun 2023 00:00:00 GMTCleiton Lira Cunha, José Nazareno Vieira Gomes, Marcus Antônio Mendonça Marrocos — We use variational methods to derive Hadamard-type formulae for the eigenvalues of a class of elliptic operators on a compact Riemannian manifold M. We then apply the latter in the following context. Consider a family of elliptic operators which is parametrized by either the set of all 𝓒^r–Riemannian metrics on M or the set of all 𝓒^r–diffeomorphisms on a domain into M. In either case, we prove that if a subset of the parametrizations set yields a simple spectrum of the operator, then it is necessarily a generic subset. We also analyse the behavior of the eigenvalues when the metric evolves along the Ricci flow on a closed Riemannian manifold, and we prove, under a suitable hypothesis, that they increaseRicci flowEigenvalues & spectrum https://arxiv.org/abs/2109.09870arxiv:2109.09870Mon, 20 Sep 2021 00:00:00 GMTJosé N. V. Gomes, Marcus A. M. Marrocos, Adrian V. C. Ribeiro — In this note, we prove triviality and nonexistence results for gradient Ricci soliton warped metrics. The proofs stem from the construction of gradient Ricci solitons that are realized as warped products, from which we know that the base spaces of these products are Ricci-Hessian type manifolds. We study this latter class of manifolds as the most appropriate setting to prove our results.Ricci solitonsRotational symmetry & warped products