From the 1 of 6 linked papers with an AI index.
6 papers
-Integrability of -Harmonic Forms and the Hopf Conjecture
Teng Huang, Weike Yu
The paper proves that on complete simply‑connected Riemannian manifolds with non‑positive sectional curvature, any L²‑harmonic form that is also L¹‑integrable must vanish, and uses…
Vafa-Witten Equations and Conformal Geometry
Teng Huang, Pan Zhang
In this article, we establish geometric and analytic constraints imposed by the existence of nontrivial solutions to the Vafa-Witten equations on closed 4-manifolds. Using conforma…
Hirzebruch -genus of compact almost Kähler manifold with negative sectional curvature
Teng Huang, Pan Zhang
Let \((X,J,Ï)\) be a closed \(2n\)-dimensional almost Kähler manifold with negative sectional curvature. We prove that if the Nijenhuis tensor of the almost complex structure is…
-Hodge theory on Complete Almost Kähler Manifolds and the Hopf Conjecture
Teng Huang, Qiang Tan, Pan Zhang
In this article, we develop an -Hodge theory on complete -dimensional almost Kähler manifolds . In the first part, we establish several identities for various L…
Schrödinger Operators, Integral Curvature, and the Euler Characteristic of Riemannian Manifolds
Teng Huang, Pan Zhang
We establish new connections between integral curvature bounds and the Euler characteristic of closed Riemannian manifolds through the perspective of Schrödinger-type operators. C…
Garding cones and positivity of curvature operators
Teng Huang, Jiaogen Zhang
This article explores the relationship between Garding cones, demonstrating that the shift cone is contained in . By combining…