https://neckpinch.com/authors/sathya-rengaswami/New arXiv papers by Sathya Rengaswami, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT 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/2303.09078arxiv:2303.09078Thu, 16 Mar 2023 00:00:00 GMTSathya Rengaswami, Mat Langford — We construct O(1)× O(n)-invariant ancient "pancake" solutions to a large and natural class of fully nonlinear curvature flows. We then establish that these are the unique O(n)-invariant ancient solutions to the corresponding flow which sweep out a slab by carrying out a fine asymptotic analysis for this class. This extends the main results of to a surprisingly general class of flows.Other curvature flowsAncient solutions https://arxiv.org/abs/2109.10456arxiv:2109.10456Tue, 21 Sep 2021 00:00:00 GMTSathyanarayanan Rengaswami — Analogous to the bowl soliton of mean curvature flow, we construct rotationally symmetric translating solutions to a very large class of extrinsic curvature flows, namely those whose speeds are α-homogeneous (α>0), elliptic and symmetric with respect to the principal curvatures. We show that these solutions are necessarily convex, and give precise criteria for the speed functions which determine whether these translators are defined on all of ℝⁿ or contained in a cylinder. For speeds that are nonzero when at least one of the principal curvatures is nonzero, we are also able to describe the asymptotics of the translator at infinity.Mean curvature flowOther curvature flowsSelf-shrinkers & translatorsHomogeneous spacesRotational symmetry & warped products