A note on harmonic forms and the boundary of the K\"ahler cone
Albert Chau, Luen-Fai Tam
TL;DR
This paper investigates the properties of harmonic forms on the boundary of the Kähler cone, demonstrating nonnegativity under specific curvature conditions, thus contributing to the understanding of Kähler geometry.
Contribution
It establishes the nonnegativity of harmonic representatives of boundary classes of the Kähler cone under certain curvature assumptions, extending previous results in Kähler geometry.
Findings
Harmonic representatives on the boundary are nonnegative under curvature conditions
Provides new insights into the structure of the Kähler cone boundary
Builds on Wu-Yau-Zheng's results in Kähler geometry
Abstract
Motivated by the results of Wu-Yau-Zheng \cite{WuYauZheng}, we show that under a certain curvature assumption the harmonic representative of any boundary class of the K\"ahler cone is nonnegative.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory