Chen Yi

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20212023

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math.DG2023

Michael-Simon Sobolev inequalities in Euclidean space

Yuting Wu, Chengyang Yi

Inspired by [1, 13], we prove Michael-Simon type inequalities for smooth symmetric uniformly positive define (0, 2)-tensor fields on compact submanifolds in Euclidean space by the…

math.DG2022

Rigidity of $4$ -dimensional complete self-shrinkers in $R^{5}$

Chengyang Yi

We show that any $4$ -dimensional complete self-shrinker in $R^{5}$ with constant squared norm $S$ of the second fundamental form, $f_{3} = 0$ and constant $f_{4}$ is isometr…

math.DG2021

The logarithmic Sobolev inequality for a submanifold in manifold with nonnegative sectional curvature

Chengyang Yi, Yu Zheng

We prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifold with nonnegative sectional curvature of arbitrary dimen…

Michael-Simon Sobolev inequalities in Euclidean space

Rigidity of 4-dimensional complete self-shrinkers in R5

The logarithmic Sobolev inequality for a submanifold in manifold with nonnegative sectional curvature

Rigidity of $4$ -dimensional complete self-shrinkers in $R^{5}$