https://neckpinch.com/authors/jose-torres-santaella/New arXiv papers by José Torres Santaella, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2512.23623arxiv:2512.23623Mon, 29 Dec 2025 00:00:00 GMTJosé Torres Santaella — We develop a rotational theory for translating solitons of fully nonlinear extrinsic curvature flows in Euclidean space. Furthermore, we obtain fine asymptotic expansions for bowl-type translators in nondegenerate and degenerate regimes. On the other hand, we also introduce a signed-neck framework which yields the construction and classification of catenoidal-type translators, distinguishing complete embedded families from maximal admissible pieces according to the selected signed branch. As applications, we prove uniqueness results for strictly convex entire graphical translators with prescribed bowl-type asymptotics and obtain catenoidal-barrier nonexistence results for bounded graphical translators.Other curvature flowsSelf-shrinkers & translatorsStability & uniquenessRotational symmetry & warped products https://arxiv.org/abs/2310.09984arxiv:2310.09984Sun, 15 Oct 2023 00:00:00 GMTSathya Rengaswami, José Torres Santaella — In this paper, we obtain the asymptotic expansion for the analogue of the bowl-soliton for a large `nondegenerate' class of fully nonlinear curvature flows. We use this to show the uniqueness of these bowl-type solitons in their asymptotic class. We also give examples to illustrate the situation for `degenerate' speeds and how they different they can be. Finally, we show how to construct `wing-like' solitons for these flows, which are complete, connected translators that are not graphical, entire or convex. We also obtain asymptotic expansions for them to show the variety of solutions that one can obtain depending on the choice of speed function.Other curvature flowsSelf-shrinkers & translatorsStability & uniqueness https://arxiv.org/abs/2306.03649arxiv:2306.03649Tue, 06 Jun 2023 00:00:00 GMTJosé Torres Santaella — In this paper we obtain several properties of translating solitons for a general class of extrinsic geometric curvature flows given by a homogeneous, symmetric, smooth non-negative function γ defined in an open cone Γ⊂ℝⁿ. The main results are tangential principles, nonexistence theorems for closed and entire solutions, and a uniqueness result that says that any strictly convex γ-translator defined on a ball with a single end 𝓒²-asymptotic to a cylinder is the "bowl"-type solution found in the translator paper of S. Rengaswami.Other curvature flowsSelf-shrinkers & translatorsHomogeneous spacesStability & uniqueness