Yu Bi

activity

20202026

most citedBi-Lipschitz Regularity of 2-Varifolds with the Critical Allard Condition

1 citations · 2 across the 15 of their papers we have counts for

collaborators

16 papers

math.DG2026

Mass-Capacity Rigidity for Asymptotically Flat Manifolds with Arbitrary Ends

Yuchen Bi

We characterize equality in the mass-capacity inequality for asymptotically flat manifolds with arbitrary ends in every dimension $n\ge 3$. If $u$ is the capacity minimizer, th…

math.DG2026

Dihedral Rigidity for Convex Polytopes by Smooth Approximation

Yuchen Bi

Following Brendle's smooth approximation approach, we give a proof of Gromov's dihedral rigidity conjecture for convex polytopes.

math.DG2026

Positive Scalar Curvature Obstructions via Singular Dimension Descent

Yuchen Bi, Jintian Zhu

In light of recent advances in conformal blow-up methods for the positive mass theorem, including He--Shi--Yu, Bi--Hao--He--Shi--Zhu, and Brendle--Wang, we develop a Schoen--Yau ty…

math.DG2026

Curvature-free effects from volume growth and ends-counting and their applications

Yuchen Bi, Jintian Zhu

In this paper, we investigate two curvature-free effects from volume growth and ends-counting, respectively. Motivated by generalizing classical results from Ricci curvature to oth…

math.DG2026

Riemannian Penrose inequality in all dimensions

Yuchen Bi, Jintian Zhu

We prove the Riemannian Penrose inequality in arbitrary dimension for smooth complete asymptotically flat manifolds with nonnegative scalar curvature and compact outer-minimizing m…

math.DG2026

A proof for the Riemannian positive mass theorem up to dimension 19

Yuchen Bi, Tianze Hao, Shihang He +2

In this paper, we prove the Riemannian positive mass theorem up to dimension $19$ , building on a combination of torical symmetrization and the singularity blow-up technique develop…

math.DG2026

Linear Quantitative Rigidity for Almost-CMC Surfaces

Yuchen Bi, Jie Zhou

We prove a quantitative rigidity result for almost constant mean curvature spheres in $R^{3}$ . Under a sub--two--sphere Willmore bound and a small $L^{2}$ --CMC defect, we show…

math.DG2025

Quantitative Stability of the Clifford Torus as a Willmore Minimizer

Yuchen Bi, Jie Zhou

For an integral $2$ -varifold $V \subset S^{3}$ with square-integrable mean curvature, unit density, and support of genus at least $1$ , assume that its Willmore energy satisfi…

math.DG2025

Mass-capacity inequality modeled on conformally flat manifolds

Yuchen Bi, Jintian Zhu

In the spin case, we can establish a mass-capacity inequality for generalized asymptotically flat manifolds $(M, g, E)$ with nonnegative scalar curvature, where the equality implies…

cond-mat.str-el2024★ 1 cited

Anomalous diffusion in quantum system driven by heavy-tailed stochastic processes

Chenyue Guo, Yuchen Bi

In this paper, we study a stochastically driven non-equilibrium quantum system where the driving protocols consist of hopping and waiting processes. The waiting times between two h…

math.DG2024

Optimal rigidity estimates for varifolds almost minimizing the Willmore energy

Yuchen Bi, Jie Zhou

For an integral $2$ -varifold $V = v (Σ, θ_{\geq 1})$ in $R^{n}$ with generalized mean curvature $H \in L^{2}$ such that $μ (R^{n}) = 4 π$ and $\int_Σ|H|^2dμ\le 16π(1+…

math.DG2022★ 1 cited

Bi-Lipschitz Regularity of 2-Varifolds with the Critical Allard Condition

Yuchen Bi, Jie Zhou

For an intergral $2$ -varifold $V = v (Σ, θ_{\geq 1})$ in the unit ball $B_{1}$ passing through the original point, assuming the critical Allard condition holds, that is, the a…

math.DG2022

Bi-Lipschitz rigidity for $L^{2}$ -almost CMC surfaces

Yuchen Bi, Jie Zhou

For smooth surfaces properly immersed in the unit ball of $\RR^n$ with density close to one and small Willmore energy, the optimal a priori estimate(bi-Lipschitz and $W^{2, 2}$ para…

math.AP2022

The $C^{0}$ -convergence at the Neumann boundary for Liouville equations

Yuchen Bi, Jiayu Li, Lei Liu +1

In this paper, we study the blow-up analysis for a sequence of solutions to the Liouville type equation with exponential Neumann boundary condition. For interior case, i.e. the blo…

math.AP2021

The Prescribed $Q$ -Curvature Flow for Arbitrary Even Dimension in a Critical Case

Yuchen Bi, Jiayu Li

In this paper, we study the prescribed $Q$ -curvature flow equation on a arbitrary even dimensional closed Riemannian manifold $(M, g)$ , which was introduced by S. Brendle in \cite{B…

math.DG2020

The asymptotic behavior of quasi-harmonic functions and eigenfunctions of the drift Laplacian

Min Chen, Jiayu Li, Yuchen Bi

The metric is quite singular at infinity and it is not complete. Using these expansions, we have a more precise description of the asymptotic behavior of quasi-harmonic functions a…

Mass-Capacity Rigidity for Asymptotically Flat Manifolds with Arbitrary Ends

Dihedral Rigidity for Convex Polytopes by Smooth Approximation

Positive Scalar Curvature Obstructions via Singular Dimension Descent

Curvature-free effects from volume growth and ends-counting and their applications

Riemannian Penrose inequality in all dimensions

A proof for the Riemannian positive mass theorem up to dimension 19

Linear Quantitative Rigidity for Almost-CMC Surfaces

Quantitative Stability of the Clifford Torus as a Willmore Minimizer

Mass-capacity inequality modeled on conformally flat manifolds

Anomalous diffusion in quantum system driven by heavy-tailed stochastic processes

Optimal rigidity estimates for varifolds almost minimizing the Willmore energy

Bi-Lipschitz Regularity of 2-Varifolds with the Critical Allard Condition

Bi-Lipschitz rigidity for L2-almost CMC surfaces

The C0-convergence at the Neumann boundary for Liouville equations

The Prescribed Q-Curvature Flow for Arbitrary Even Dimension in a Critical Case

The asymptotic behavior of quasi-harmonic functions and eigenfunctions of the drift Laplacian

Bi-Lipschitz rigidity for $L^{2}$ -almost CMC surfaces

The $C^{0}$ -convergence at the Neumann boundary for Liouville equations

The Prescribed $Q$ -Curvature Flow for Arbitrary Even Dimension in a Critical Case