https://neckpinch.com/authors/chaoqun-gao/New arXiv papers by Chaoqun Gao, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2608.11841arxiv:2608.11841Wed, 12 Aug 2026 00:00:00 GMTChaoqun Gao, Yong Wei, Rong Zhou — We prove sharp Weinstock inequalities for the first nonzero Steklov eigenvalue of smooth outward-minimizing domains in Euclidean space and hyperbolic space. The method is based on the weak inverse mean curvature flow of Huisken–Ilmanen. The main new ingredient is an endpoint distributional monotonicity argument obtained from the calibrated weak formulation and the Gauss–Green formula for divergence-measure fields.Mean curvature flowOther curvature flowsInverse mean curvature flowEigenvalues & spectrum https://arxiv.org/abs/2607.02067arxiv:2607.02067Thu, 02 Jul 2026 00:00:00 GMTChaoqun Gao, Yong Wei, Rong Zhou — We prove an anisotropic analogue of the higher regularity theorem of Huisken and Ilmanen for inverse mean curvature flow. For an arbitrary smooth Minkowski norm, we first prove a Huisken–Ilmanen type Harnack estimate for smooth closed strictly star-shaped solutions. We then construct global smooth solutions starting from C¹ strictly star-shaped hypersurfaces with bounded nonnegative weak anisotropic mean curvature. Combining this construction with the asymptotic theory for weak inverse anisotropic mean curvature flow, we show that weak solutions starting from bounded smooth initial sets become smooth outside a compact set.Mean curvature flowOther curvature flowsInverse mean curvature flowAnisotropic & nonlocal flowsHarnack inequalitiesWeak & singular flows https://arxiv.org/abs/2510.08168arxiv:2510.08168Thu, 09 Oct 2025 00:00:00 GMTChaoqun Gao, Yong Wei, Rong Zhou — We first establish a local gradient estimate for anisotropic p-harmonic functions. A key feature of our estimate is that the constant remains bounded as p→ 1; consequently, in the limit p→ 1, this estimate yields the local gradient estimate for weak solutions of the inverse anisotropic mean curvature flow (IAMCF). As an application, we show that the weak IAMCF is asymptotic to the expanding Wulff shape solution at the infinity, thereby extending the result of Huisken and Ilmanen in [8] to the anisotropic case.Mean curvature flowAnisotropic & nonlocal flowsWeak & singular flows