https://neckpinch.com/authors/bo-yang/New arXiv papers by Bo Yang, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2507.12097arxiv:2507.12097Wed, 16 Jul 2025 00:00:00 GMTShujing Pan, Bo Yang — In this paper, we study inverse curvature flows for strictly convex, capillary hypersurfaces in the unit Euclidean ball. We establish the existence and convergence results for a class of such flows. As an application, we derive a family of Alexandrov Fenchel inequalities for weakly convex hypersurfaces with free boundary.Other curvature flowsInverse mean curvature flowFree boundary & capillaryGeometric inequalities https://arxiv.org/abs/2406.05159arxiv:2406.05159Thu, 06 Jun 2024 00:00:00 GMTYong Wei, Bo Yang, Tailong Zhou — We consider the volume preserving flow of smooth, closed and convex hypersurfaces in the hyperbolic space ℍⁿ⁺¹ with speed given by a general nonhomogeneous function of the Gauss curvature. For a large class of speed functions, we prove that the solution of the flow remains convex, exists for all positive time t∈ [0,∞) and converges to a geodesic sphere exponentially as t→∞ in the smooth topology. A key step is to show the L¹ oscillation decay of the Gauss curvature to its average along a subsequence of times going to the infinity, which combined with an argument using the hyperbolic curvature measure theory implies the Hausdorff convergence.Other curvature flowsGauss curvature flowVolume-preserving & constrained flowsHomogeneous spacesLong-time existence & convergence https://arxiv.org/abs/2404.13670arxiv:2404.13670Sun, 21 Apr 2024 00:00:00 GMTShujing Pan, Bo Yang — We prove a Minkowski type inequality for weakly mean convex and star-shaped hypersurfaces in warped cylinders which are asymptotically flat or hyperbolic. In particular, we show that this sharp inequality holds for outward minimizing hypersurfaces in the Schwarzschild manifold or the hyperbolic space using the weak solution of the inverse mean curvature flow.Mean curvature flowOther curvature flowsInverse mean curvature flowWeak & singular flowsBoundaries & non-compactGeometric inequalities https://arxiv.org/abs/2311.02364arxiv:2311.02364Sat, 04 Nov 2023 00:00:00 GMTShujing Pan, Bo Yang — We consider a locally constrained curvature flow in a static rotationally symmetric space Nⁿ⁺¹, which was firstly introduced by Hu and Li in the hyperbolic space. We prove that if the initial hypersurface is graphical, then the smooth solution of the flow remains to be graphical, exists for all positive time t∈[0,∞) and converges to a slice of Nⁿ⁺¹ exponentially in the smooth topology. Moreover, we prove that the flow preserves static convexity if the initial hypersurface is close to a slice of Nⁿ⁺¹ in the C¹ sense. As applications, we prove a family of weighted geometric inequalities for static convex domains which is close to a slice of Nⁿ⁺¹ in the C¹ sense.Other curvature flowsVolume-preserving & constrained flowsLong-time existence & convergenceRotational symmetry & warped productsGeometric inequalities https://arxiv.org/abs/2210.06035arxiv:2210.06035Wed, 12 Oct 2022 00:00:00 GMTYong Wei, Bo Yang, Tailong Zhou — We consider the volume preserving flow of smooth, closed and convex hypersurfaces in the hyperbolic space ℍⁿ⁺¹ (n≥ 2) with the speed given by arbitrary positive power α of the Gauss curvature. We prove that if the initial hypersurface is convex, then the smooth solution of the flow remains convex and exists for all positive time t∈ [0,∞). Moreover, we apply a result of Kohlmann which characterises the geodesic ball using the hyperbolic curvature measures and an argument of Alexandrov reflection to prove that the flow converges to a geodesic sphere exponentially in the smooth topology. This can be viewed as the first result for non-local type volume preserving curvature flows for hypersurfaces in the hyperbolic space with only convexity required on the initial data.Other curvature flowsGauss curvature flowVolume-preserving & constrained flowsLong-time existence & convergence https://arxiv.org/abs/2209.12479arxiv:2209.12479Mon, 26 Sep 2022 00:00:00 GMTYingxiang Hu, Yong Wei, Bo Yang, Tailong Zhou — In this paper, we study the locally constrained inverse curvature flow for hypersurfaces in the half-space with θ-capillary boundary, which was recently introduced by Wang-Weng-Xia. Assume that the initial hypersurface is strictly convex with the contact angle θ∈ (0,π/2]. We prove that the solution of the flow remains to be strictly convex for t>0, exists for all positive time and converges smoothly to a spherical cap. As an application, we prove a complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space with the contact angle θ∈(0,π/2]. Along the proof, we develop a new tensor maximum principle for parabolic equations on compact manifold with proper Neumann boundary condition.Other curvature flowsInverse mean curvature flowVolume-preserving & constrained flowsBoundaries & non-compactFree boundary & capillaryLong-time existence & convergenceGeometric inequalities