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arXiv · 2606.19806

The top Yau--Yang conjecture for K\"ahler manifolds with positive sectional curvature

Ved V. Datar·Vamsi P. Pingali·Harish Seshadri
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Abstract

We prove that the top wedge power of the Ricci form of a complete non-compact K\"ahler manifold with positive sectional curvature has finite integral. Using a result of Chen-Zhu, an immediate consequence is the quasiprojectivity of such manifolds under the assumption of bounded sectional curvature. A key new idea to prove B\'ezout estimates along with a Lipschitz weight with finite Monge-Amp\`ere mass is used in the proof of the main result.

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Ved V. Datar, Vamsi P. Pingali, Harish Seshadri. 2026-06-18. The top Yau--Yang conjecture for K\"ahler manifolds with positive sectional curvature. https://arxiv.org/abs/2606.19806

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