Zobrazeno 1 - 10
of 161
pro vyhledávání: '"Xu, Guoyi"'
Autor:
Wang, Haibin, Xu, Guoyi
We prove the sharp lower bound of the first Neumann eigenvalue for bounded convex planar domain in term of its diameter and width.
Comment: reference and Remark 1.4 is added
Comment: reference and Remark 1.4 is added
Externí odkaz:
http://arxiv.org/abs/2407.13984
Autor:
Xu, Guoyi
For a geodesic ball with non-negative Ricci curvature and mean convex boundary, it is known that the first Dirichlet eigenvalue of this geodesic ball has a sharp lower bound in term of its radius. We show a quantitative explicit inequality, which bou
Externí odkaz:
http://arxiv.org/abs/2407.10027
Autor:
Li, Weiying, Xu, Guoyi
We establish the extrinsic Bonnet-Myers Theorem for compact Riemannian manifolds with positive Ricci curvature. And we show the almost rigidity for compact hypersurfaces, which have positive sectional curvature and almost maximal extrinsic diameter i
Externí odkaz:
http://arxiv.org/abs/2405.04822
Autor:
Xu, Guoyi, Xue, Xiaolong
On compact Riemannian manifolds with non-negative Ricci curvature and smooth (possibly empty), convex (or mean convex) boundary, if the sharp Li-Yau type gradient estimate of an Neumann (or Dirichlet) eigenfunction holds at some non-critical points o
Externí odkaz:
http://arxiv.org/abs/2405.05517
Publikováno v:
Transactions of the American Mathematical Society,2024
For three dimensional complete, non-compact Riemannian manifolds with non-negative Ricci curvature and uniformly positive scalar curvature, we obtain the sharp linear volume growth ratio and the corresponding rigidity.
Comment: submitted to some
Comment: submitted to some
Externí odkaz:
http://arxiv.org/abs/2405.04001
Autor:
Xu, Guoyi
Publikováno v:
Proceedings of the American Mathematical Society,2023
On any complete three dimensional Riemannian manifold with a pole and non-negative Ricci curvature, we show that the asymptotic scaling invariant integral of scalar curvature, is equal to a term determined by the asymptotic volume ratio of this Riema
Externí odkaz:
http://arxiv.org/abs/2306.07460
Publikováno v:
Calc. Var. Partial Differential Equations 62 (2023), no. 3, Paper No. 75, 42 pp
For a geodesic ball with non-negative Ricci curvature and almost maximal volume, without using compactness argument, we construct an $\epsilon$-splitting map on a concentric geodesic ball with uniformly small radius. There are two new technical point
Externí odkaz:
http://arxiv.org/abs/2212.10759
In this note, we obtain the rigidity of the sharp Cheng-Yau gradient estimate for positive harmonic functions on surfaces with nonegative Gaussian curvature, the rigidity of the sharp Li-Yau gradient estimate for positive solutions to heat equations
Externí odkaz:
http://arxiv.org/abs/2208.02944
Publikováno v:
Math. Z. 300, (2022),no. 2, 2063-2068
On complete noncompact Riemannian manifolds with non-negative Ricci curvature, Li-Schoen proved the uniform Poincare inequality for any ge odesic ball. In this note, we obtain the sharp lower bound of the first Dirichlet eigenvalue of such geodesic b
Externí odkaz:
http://arxiv.org/abs/2108.06951
Autor:
Xu, Guoyi
Publikováno v:
J. Lond. Math. Soc. (2) 101 (2020), no. 3, 1298-1319
We study the growth rate of harmonic functions in two aspects: gradient estimate and frequency. We obtain the sharp gradient estimate of positive harmonic function in geodesic ball of complete surface with nonnegative curvature. On complete Riemannia
Externí odkaz:
http://arxiv.org/abs/1912.02627