arXiv subjects

Yinhang Wang

Publications and source records attributed to Yinhang Wang.

3 recordsLinked to original sources

arXiv2025

On the new weighted geometric inequalities near the sphere in space forms

In this paper, we first investigate weighted Minkowski type inequalities for nearly spherical sets in space forms, focusing on the sets that are $C^1$-close to geodesic spheres. Our results generalize the work of \cite{G22} by incorporating broader geometric settings and convex weight functions. Additionally, we establish quantitative stability estimates for weighted Alexandrov-Fenchel type inequalities in $\mathbb{R}^{n+1}$ and $\mathbb{H}^{n+1}$, extending the earlier results of \cite{VW24} and \cite{ZZ23}. These inequalities hold for nearly spherical sets that are $W^{2,\infty}$-close to geodesic spheres coupled with general convex weights.

math.DG↗

arXiv2025

On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds

In this paper, we give some new characterizations of umbilic hypersurfaces in general warped product manifolds, which can be viewed as generalizations of the work in \cite{KLP18} and \cite{WX14}. Firstly, we prove the rigidity for hypersurfaces with constant linear combinations of shifted higher order mean curvatures. Using integral inequalities and Minkowski-type formulas, we then derive rigidity theorems in sub-static warped product manifolds, including cases that the hypersurface satisfies some nonlinear curvature conditions. Finally, we show that our results can be applied to more general warped product manifolds, including the cases with non-constant sectional curvature fiber.

math.DG↗

arXiv2024

On rigidity of hypersurfaces with constant shifted curvature functions in hyperbolic space

In this paper, we first give some new characterizations of geodesic spheres in the hyperbolic space by the condition that hypersurface has constant weighted shifted mean curvatures, or constant weighted shifted mean curvature ratio, which generalize the result of Hu-Wei-Zhou \cite{HWZ23}. Secondly, we investigate several rigidity problems for hypersurfaces in the hyperbolic space with constant linear combinations of weighted shifted mean curvatures as well as radially symmetric shifted mean curvatures. As applications, we obtain the rigidity results for hypersurfaces with constant linear combinations of mean curvatures in a general form and constant Gauss-Bonnet curvature $L_k$ under weaker conditions, which extend the work of the third author and Xia \cite{WX14}.

math.DG↗