https://neckpinch.com/authors/sara-albert-niclos/New arXiv papers by Sara Albert-Niclòs, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2608.10745/arxiv:2608.10745Tue, 11 Aug 2026 00:00:00 GMTSara Albert-Niclòs, Esther Cabezas-Rivas, Shujing Pan — We introduce fully nonlinear curvature flows of horo-convex hypersurfaces in the sphere that preserve an arbitrarily prescribed spherical quermassintegral. The non-local normalization is defined relative to a fixed ambient origin, and we prove that the evolution is governed by a single smooth fixed-origin equation for all time. For monotone, homogeneous curvature functions satisfying concavity and inverse concavity, we establish preservation of horo-convexity, uniform curvature pinching, a direct estimate for the non-local coefficient. A Tso-type argument then yields global curvature bounds and long-time existence. We further prove exponential decay of the traceless second fundamental form and exponential C^∞ convergence to the geodesic sphere centered at the fixed origin whose radius is determined by the preserved quermassintegral.Other curvature flowsCurvature pinchingHomogeneous spacesLong-time existence & convergenceGeometric inequalities https://neckpinch.com/papers/2604.13734/arxiv:2604.13734Wed, 15 Apr 2026 00:00:00 GMTSara Albert-Niclòs, Esther Cabezas-Rivas — We study area- and length-preserving curvature flows for embedded closed curves on pinched Hadamard surfaces. In the variable-curvature setting, the evolution equations contain additional lower-order terms, so the PDE analysis requires refined comparison arguments and delicate curvature estimates. For smooth convex initial curves, we prove preservation and instantaneous strictness of convexity, long-time existence, and uniform bounds for the curvature and its higher derivatives. Under additional geometric assumptions, we obtain convergence of the curvature to a constant. In the rotationally symmetric case, the area-preserving flow exhibits a dichotomy: either the evolving curves converge exponentially to a geodesic circle, or they drift off to infinity and approach a constant-curvature limit curve. We also identify a geometric condition on the initial curve that prevents escape to infinity and guarantees convergence to a geodesic circle.Other curvature flowsVolume-preserving & constrained flowsLong-time existence & convergenceRotational symmetry & warped products