Teng Huang

activity

20182026

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7 papers · 1 filter

math.DG2026

$L^{1}$ -Integrability of $L^{2}$ -Harmonic Forms and the Hopf Conjecture

Teng Huang, Weike Yu

In this note, we study $L^{2}$ -harmonic forms on complete simply-connected Riemannian manifolds with non-positive sectional curvature. We first establish an a priori $L^{\infty}$ -e…

math.DG2026

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…

math.DG2026

Hirzebruch $χ_{y}$ -genus of compact almost Kähler manifold with negative sectional curvature

Teng Huang, Pan Zhang

Let $(X,J,ω)$ 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 su…

math.DG2026

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. Ce…

math.DG2025

Garding cones and positivity of curvature operators

Teng Huang, Jiaogen Zhang

This article explores the relationship between Garding cones, demonstrating that the shift cone $Γ_{2}^{+} (α)$ is contained in $P_{m}$ . By combining t…

math.DG2023

$L^{2}$ -Hodge theory on Complete Almost Kähler Manifolds and the Hopf Conjecture

Teng Huang, Qiang Tan, Pan Zhang

In this article, we develop an $L^{2}$ -Hodge theory on complete $2 n$ -dimensional almost Kähler manifolds $(X, ω)$ . In the first part, we establish several identities for various Lap…

math.DG2018

$L^{2}$ harmonic forms on complete special holonomy manifolds

Teng Huang

In this article, we consider $L^{2}$ harmonic forms on a complete non-compact Riemannian manifold $X$ with a nonzero parallel form $ω$ . The main result is that if $(X, ω)$ is a comp…

L1-Integrability of L2-Harmonic Forms and the Hopf Conjecture

Vafa-Witten Equations and Conformal Geometry

Hirzebruch χy​-genus of compact almost Kähler manifold with negative sectional curvature

Schrödinger Operators, Integral Curvature, and the Euler Characteristic of Riemannian Manifolds

Garding cones and positivity of curvature operators

L2-Hodge theory on Complete Almost Kähler Manifolds and the Hopf Conjecture

L2 harmonic forms on complete special holonomy manifolds

$L^{1}$ -Integrability of $L^{2}$ -Harmonic Forms and the Hopf Conjecture

Hirzebruch $χ_{y}$ -genus of compact almost Kähler manifold with negative sectional curvature

$L^{2}$ -Hodge theory on Complete Almost Kähler Manifolds and the Hopf Conjecture

$L^{2}$ harmonic forms on complete special holonomy manifolds