https://neckpinch.com/authors/ya-gao/New arXiv papers by Ya Gao, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2408.07949arxiv:2408.07949Thu, 15 Aug 2024 00:00:00 GMTYa Gao, Jing Mao — For a given smooth convex cone in the Euclidean (n+1)-space ℝⁿ⁺¹ which is centered at the origin, we investigate the evolution of strictly mean convex hypersurfaces, which are star-shaped with respect to the center of the cone and which meet the cone perpendicularly, along an inverse curvature flow with the speed equal to (f(r)H)⁻¹, where f is a positive function of the radial distance parameter r and H is the mean curvature of the evolving hypersurfaces. The evolution of those hypersurfaces inside the cone yields a fully nonlinear parabolic Neumann problem. Under suitable constraints on the first and the second derivatives of the radial function f, we can prove the long-time existence of this flow, and moreover the evolving hypersurfaces converge smoothly to a piece of the round sphere.Other curvature flowsInverse mean curvature flowFree boundary & capillaryLong-time existence & convergence https://arxiv.org/abs/2109.02191arxiv:2109.02191Mon, 06 Sep 2021 00:00:00 GMTYa Gao, Chenyang Liu, Jing Mao — In this paper, we consider the evolution of spacelike graphic curves defined over a piece of hyperbola 𝓗¹(1), of center at origin and radius 1, in the 2 dimensional Lorentz-Minkowski plane ℝ²₁ along an anisotropic inverse mean curvature flow with the vanishing Neumann boundary condition, and prove that this flow exists for all the time. Moreover, we can show that, after suitable rescaling, the evolving spacelike graphic curves converge smoothly to a piece of hyperbola of center at origin and prescribed radius, which actually corresponds to a constant function defined over the piece of 𝓗¹(1), as time tends to infinity.Mean curvature flowOther curvature flowsInverse mean curvature flowBoundaries & non-compactFree boundary & capillaryLong-time existence & convergencePhysics https://arxiv.org/abs/2108.08686arxiv:2108.08686Thu, 19 Aug 2021 00:00:00 GMTYa Gao, Jing Mao — In this paper, we consider the evolution of spacelike graphic hypersurfaces defined over a convex piece of hyperbolic plane 𝓗ⁿ(1), of center at origin and radius 1, in the (n+1)-dimensional Lorentz-Minkowski space ℝⁿ⁺¹₁ along the inverse Gauss curvature flow (i.e., the evolving speed equals the (−1/n)-th power of the Gaussian curvature) with the vanishing Neumann boundary condition, and prove that this flow exists for all the time. Moreover, we can show that, after suitable rescaling, the evolving spacelike graphic hypersurfaces converge smoothly to a piece of the spacelike graph of a positive constant function defined over the piece of 𝓗ⁿ(1) as time tends to infinity.Other curvature flowsGauss curvature flowBoundaries & non-compactFree boundary & capillaryLong-time existence & convergencePhysics