Geodesic Rays in the Donaldson--Uhlenbeck--Yau Theorem

Mattias Jonsson; Nicholas McCleerey; Sanal Shivaprasad

Geodesic Rays in the Donaldson--Uhlenbeck--Yau Theorem

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arxiv 2210.09246 v2 pith:KZH5B35R submitted 2022-10-17 math.DG math.CV

Mattias Jonsson , Nicholas McCleerey , Sanal Shivaprasad This is my paper · ORCID

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keywords donaldson--uhlenbeck--yaugeodesicproofsraystheoremconjecturegivehermitian

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We give new proofs of two implications in the Donaldson--Uhlenbeck--Yau theorem. Our proofs are based on geodesic rays of Hermitian metrics, inspired by recent work on the Yau--Tian--Donaldson conjecture.

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Constructing stable Hilbert bundles via Diophantine approximation
math.DG 2025-01 conditional novelty 8.0 of 10

For any compact Riemann surface of positive genus and any irrational slope θ, the colimit of stable bundles whose slopes are even convergents of θ completes to a holomorphic Hilbert bundle with a Hermitian-Einstein metric.

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