arXiv subjects

Yunqing Wu

Publications and source records attributed to Yunqing Wu.

5 recordsLinked to original sources

arXiv2026

Shortest closed geodesics on three-dimensional isospectral manifolds

We prove that the spectrum of a smooth closed three-manifold gives a positive lower bound for the length of its shortest nonconstant closed geodesic. The argument uses three curvature heat coefficients and the first positive singularity of the retarded wave trace. The heat coefficients yield a curvature--length dichotomy: sufficiently large maximum curvature forces a closed geodesic shorter than the curvature scale. We then show that a shortest closed geodesic lying below the conjugate radius produces a singularity of the sine trace. Combining these estimates gives a lower bound depending only on the common spectrum. The compactness theorem of Anderson then implies smooth compactness of the full isospectral family modulo diffeomorphisms.

math.DG↗

arXiv2024

Prescribing negative curvature with cusps and conical singularities on compact surface

On a compact surface, we prove existence and uniqueness of the conformal metric whose curvature is prescribed by a negative function away from finitely many points where the metric has prescribed angles presenting cusps or conical singularities.

math.DG↗

arXiv2024

Estimates for complex singular Monge-Ampère equations via integral method

In this paper, we obtain gradient estimates and Laplacian estimates for the solution to the singular complex Monge-Ampère equation by applying the integral method.

math.DG↗

arXiv2024

Prescribing positive curvature with conical singularities on $\mathbb S^2$

For conformal metrics with conical singularities and positive curvature on $\mathbb S^2$, we prove a convergence theorem and apply it to obtain a criterion for nonexistence in an open region of the prescribing data. The core of our study is a fine analysis of the bubble trees and an area identity in the convergence process.

math.DG↗

arXiv2022

Classification of Willmore surfaces with vanishing Gaussian curvature

We classify simply-connected, complete Willmore surfaces with vanishing Gaussian curvature. We also study the Willmore cones and give a classification. As an application, we give a Bernstein-type theorem.

math.DG↗