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Adam Jacob

Publications and source records attributed to Adam Jacob.

22 records · Page 2Linked to original sources
arXiv2013

Existence of approximate Hermitian-Einstein structures on semi-stable bundles

The purpose of this paper is to investigate canonical metrics on a semi-stable vector bundle E over a compact Kahler manifold X. It is shown that, if E is semi-stable, then Donaldson's functional is bounded from below. This implies that E admits an approximate Hermitian-Einstein structure, generalizing a classic result of Kobayashi for projective manifolds to the Kahler case. As an application some basic properties of semi-stable vector bundles over compact Kahler manifolds are established, such as the fact that semi-stability is preserved under tensor product and certain exterior and symmetric products.

math.DG↗
arXiv2013

The limit of the Yang-Mills flow on semi-stable bundles

By the work of Hong and Tian it is known that given a holomorphic vector bundle E over a compact Kahler manifold X, the Yang-Mills flow converges away from an analytic singular set. If E is semi-stable, then the limiting metric is Hermitian-Einstein and will decompose the limiting bundle into a direct sum of stable bundles. Bando and Siu prove this limiting bundle can be extended to a reflexive sheaf E' on all of X. In this paper, we construct an isomorphism between E' and the double dual of the stable quotients of the graded Seshadri filtration of E.

math.DG↗
arXiv2011

On the convergence of the Sasaki-Ricci flow

Given a Sasaki manifold S, we prove the Sasaki-Ricci flow converges exponentially fast to a Sasaki-Einstein metric if one exists, provided the automorphism group of the transverse holomorphic structure is trivial.

math.DG↗