https://neckpinch.com/authors/g-pacelli-bessa/New arXiv papers by G. Pacelli Bessa, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2601.08661/arxiv:2601.08661Tue, 13 Jan 2026 00:00:00 GMTHilário Alencar, G. Pacelli Bessa, Gregório Silva Neto — In this paper, we establish nonexistence results for complete translating solitons of the r-mean curvature flow under suitable growth conditions on the (r-1)-mean curvature and on the norm of the second fundamental form. We first show that such solitons cannot be entirely contained in the complement of a right rotational cone whose axis of symmetry is aligned with the translation direction. We then relax the growth condition on the (r-1)-mean curvature and prove that properly immersed translating solitons cannot be confined to certain half-spaces opposite to the translation direction. We conclude the paper by showing that complete, properly immersed translating solitons satisfying appropriate growth conditions on the (r-1)-mean curvature cannot lie completely within the intersection of two transversal vertical half-spaces.Mean curvature flowSelf-shrinkers & translators https://neckpinch.com/papers/2402.09627/arxiv:2402.09627Thu, 15 Feb 2024 00:00:00 GMTHilário Alencar, G. Pacelli Bessa, Gregório Silva Neto — In this paper, we prove gap results for complete self-shrinkers of the r-mean curvature flow involving a modified second fundamental form. These results extend previous results for self-shrinkers of the mean curvature flow due to Cao-Li and Cheng-Peng. To prove our results we show that, under suitable curvature bounds, proper self-shrinkers are parabolic for a certain second-order differential operator which generalizes the drifted Laplacian and, even if is not proper, this differential operator satisfies an Omori-Yau type maximum principle.Mean curvature flowSelf-shrinkers & translators