https://neckpinch.com/authors/shujing-pan/New arXiv papers by Shujing Pan, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2608.10745arxiv: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://arxiv.org/abs/2604.15993arxiv:2604.15993Fri, 17 Apr 2026 00:00:00 GMTShujing Pan, Julian Scheuer — This paper is about hypersurfaces with boundary lying in the Euclidean unit ball, which meet the unit sphere at a fixed angle θ∈(0,fracπ2]. Such hypersurfaces are called θ-capillary hypersurfaces and for those we introduce a new notion of convexity, which we call θ-horocap-convexity. For such hypersurfaces, we prove the convergence of a curvature flow of Guan/Li type with capillary boundary. Remarkably, we prove this result for a class of curvature functions which include all quotients of symmetric polynomials and, as a consequence, we obtain the full set of quermassintegral inequalities in the θ-horocap-convex case. In the strictly horocap-convex setting, we employ the flow to prove the geometric inequalities, while for the horocap-convex case and the characterization of the equality case, we develop new arguments which are interesting in their own right.Other curvature flowsFree boundary & capillaryGeometric inequalities 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/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/2404.10298arxiv:2404.10298Tue, 16 Apr 2024 00:00:00 GMTShujing Pan, Yong Wei — In this paper, we consider the anisotropic α-Gauss curvature flow for complete noncompact convex hypersurfaces in the Euclidean space with the anisotropy determined by a smooth closed uniformly convex Wulff shape. We show that for all positive power α>0, if the initial hypersurface is complete noncompact and locally uniformly convex, then the solution of the flow exists for all positive time.Other curvature flowsGauss curvature flowAnisotropic & nonlocal flowsBoundaries & non-compactLong-time existence & convergence 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