https://neckpinch.com/authors/aprameya-girish-hebbar/New arXiv papers by Aprameya Girish Hebbar, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2609.10197arxiv:2609.10197Wed, 09 Sep 2026 00:00:00 GMTAprameya Girish Hebbar, Guanhua Shao, Qi Sun — We show that on any closed orientable real-analytic Riemannian surface, any smoothly immersed closed immortal curve-shortening flow converges to a unique non-constant closed geodesic.Curve shorteningLong-time existence & convergence https://arxiv.org/abs/2605.14905arxiv:2605.14905Thu, 14 May 2026 00:00:00 GMTAprameya Girish Hebbar — We show that κ-solutions to the Ricci flow in dimensions n≥ 4 whose asymptotic shrinking Ricci soliton is the round cylinder Sⁿ⁻¹×ℝ must be uniformly PIC. Combined with earlier classification results, this implies that any such noncompact solution is either the round shrinking cylinder or the Bryant steady soliton, and any such compact solution is Perelman's ancient solution.Ricci flowRicci solitonsAncient solutionsSphere theoremsBoundaries & non-compact https://arxiv.org/abs/2603.21397arxiv:2603.21397Sun, 22 Mar 2026 00:00:00 GMTAprameya Girish Hebbar, Natasa Sesum — In this paper we study the behavior of the scalar curvature at infinity on complete noncompact steady gradient Ricci solitons. In dimension four, we assume that the canonical Ricci flow induced by the soliton is a weak κ-solution and that the soliton is not isometric to the Bryant soliton. In this setting, we identify the two edges of the soliton and prove that the scalar curvature decays at a linear rate away from these edges. Moreover, if the scalar curvature vanishes at infinity, then a stronger inequality holds and the asymptotic cone is a ray. In particular, our results apply to the four-dimensional steady solitons constructed by Lai.Ricci flowRicci solitonsAncient solutions4-manifoldsScalar curvatureBoundaries & non-compact