https://neckpinch.com/authors/gang-li/New arXiv papers by Gang Li, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2604.20383arxiv:2604.20383Wed, 22 Apr 2026 00:00:00 GMTGang Li — This is a continuation of the research in [16]. Let (M,g₋₁) be a closed geodesic r₀-ball in the hyperbolic space (ℍⁿ,g₋₁). Let m≠1 be a positive constant. In this paper, we show that for n≥3, starting from the metric m g₋₁ on M, with certain prescribed non-decreasing rotationally symmetric mean curvature and the fixed conformal class [g_(Sⁿ⁻¹)] on the boundary ∂M, the solution g(t) to the normalized Ricci flow (1.2) which is continuous up to the boundary, exists for all t>0, and converges locally uniformly in the interior M of M to a complete hyperbolic metric as t→∞(see Theorem 1.1 for details). Under some additional conditions, we show the same conclusion holds for n=2.Ricci flowBoundaries & non-compactRotational symmetry & warped products https://arxiv.org/abs/2604.20375arxiv:2604.20375Wed, 22 Apr 2026 00:00:00 GMTGang Li — In this paper, we show that starting from a geodesic ball overlineB_(r₀)(0) in ℍⁿ, for n≥3, with prescribed non-decreasing rotationally symmetric mean curvature and the fixed conformal class [g_(Sⁿ⁻¹)] on the boundary, the solution g(t) to the normalized Ricci flow (1.2) which is continuous up to the boundary, exists for all t>0 and converges locally uniformly in B_(r₀)(0) to a complete hyperbolic metric as t→∞(see Theorem 1.2 for details). Moreover, the sectional curvature of g(t) maintains less than −1 for t>0. For dimension 2, to achieve such a convergence result, we need the additional assumption that the mean curvature on the boundary increases in a certain speed to infinity as t→∞.Ricci flowBoundaries & non-compactRotational symmetry & warped products https://arxiv.org/abs/2502.00660arxiv:2502.00660Sun, 02 Feb 2025 00:00:00 GMTGang Li — Let (M,g₀) be a 2-D compact surface with boundary ∂M and its interior M. We show that for a large class of initial and boundary data, the initial-boundary value problem of the normalized Ricci flow (1.10)−(1.12), with prescribed geodesic curvature ψ on ∂M, has a unique solution for all t>0, and it converges to the complete hyperbolic metric locally uniformly in M. Here the natural condition that ψ>0 causes the main difficulty in the a priori estimates in the corresponding initial-boundary problem (1.15)−(1.17) of the parabolic equations, for which an auxiliary Cauchy-Dirichlet problem is introduced. We also provide examples of the boundary data ψ which fits well with the natural asymptotic behavior of the geodesic curvature, but the solution to (1.10)−(1.12) fails to converge to the complete hyperbolic metric.Ricci flowSurfaces