Ping Li

activity

20232026

collaborators

10 papers

math.AG2026

Topological obstructions to geometric positivity and negativity on Calabi-Yau manifolds

Ping Li

We study whether the topology underlying a Calabi-Yau manifold can support natural geometric positivity or negativity structures. In even complex dimension $n \geq 4$ (assuming $b_…

math.DG2026

The $χ_{y}$ -genus, Chern number inequalities and signature

Ping Li, Yibo Ren

This article has two parts. In the first part we introduce two positivity conditions for the modified $χ_{y}$ -genus on almost-complex manifolds and show that each of them implies a f…

math.DG2025

Hamiltonian circle action, invariant hypersurface and the complex projective space

Ping Li

Let $M$ be a $2 n$ -dimensional closed symplectic manifold admitting a Hamiltonian circle action with isolated fixed points. We show that if $M$ contains an $S^{1}$ -invariant symplecti…

math.CO2025

Planar Turán numbers of three configurations

Xuqing Bai, Zhipeng Gao, Ping Li

The planar Tuán number of $H$ , denoted by $e x_{P} (n, H)$ , is defined as the maximum number of edges in an $n$ -vertex $H$ -free planar graph. The exact value of $ex_{\mathca…

math.CO2025

Dense $2$ -connected planar graphs and the planar Turán number of $2 C_{k}$

Ping Li

Shi, Walsh and Yu demonstrated that any dense planar graph with certain property (known as circuit graph) contains a large near-triangulation. We extend the result to $2$ -connected…

math.AG2025

Compactification of homology cells, Fujita's conjectures and the complex projective space

Ping Li, Thomas Peternell

We show that a compact Kähler manifold $M$ containing a smooth connected divisor $D$ such that $M ∖ D$ is a homology cell, e.g., contractible, must be projective space with…

math.DG2025

Chern numbers on positive vector bundles and combinatorics

Ping Li

Combinatorial ideas are developed in this article to study Chern numbers on ample and numerically effective vector bundles. An effective lower bound for Chern numbers of ample vect…

math.DG2024

Explicit formulas for the Hattori-Stong theorem and applications

Ping Li, Wangyang Lin

We employ combinatorial techniques to present an explicit formula for the coefficients in front of Chern classes involving in the Hattori-Stong integrability conditions. We also gi…

math.DG2023

The spectral rigidity of Ricci soliton and Einstein-type manifolds

Ping Li, Xiaomei Sun, Anqiang Zhu

We are concerned in this article with a classical topic in spectral geometry dating back to McKean-Singer, Patodi and Tanno: whether or not the constancy of sectional curvature (re…

cs.DS2023

Faster Algorithms for Generalized Mean Densest Subgraph Problem

Chenglin Fan, Ping Li, Hanyu Peng

The densest subgraph of a large graph usually refers to some subgraph with the highest average degree, which has been extended to the family of $p$ -means dense subgraph objectives…

Topological obstructions to geometric positivity and negativity on Calabi-Yau manifolds

The χy​-genus, Chern number inequalities and signature

Hamiltonian circle action, invariant hypersurface and the complex projective space

Planar Turán numbers of three configurations

Dense 2-connected planar graphs and the planar Turán number of 2Ck​

Compactification of homology cells, Fujita's conjectures and the complex projective space

Chern numbers on positive vector bundles and combinatorics

Explicit formulas for the Hattori-Stong theorem and applications

The spectral rigidity of Ricci soliton and Einstein-type manifolds

Faster Algorithms for Generalized Mean Densest Subgraph Problem

The $χ_{y}$ -genus, Chern number inequalities and signature

Dense $2$ -connected planar graphs and the planar Turán number of $2 C_{k}$