1 citations · 2 across the 15 of their papers we have counts for
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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…
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.
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…
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…
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…
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 , building on a combination of torical symmetrization and the singularity blow-up technique develop…
Linear Quantitative Rigidity for Almost-CMC Surfaces
Yuchen Bi, Jie Zhou
We prove a quantitative rigidity result for almost constant mean curvature spheres in . Under a sub--two--sphere Willmore bound and a small --CMC defect, we show…