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11 papers · 1 filter
Heat kernel on Ricci shrinkers
Yu Li, Bing Wang
In this paper, we systematically study the heat kernel of the Ricci flows induced by Ricci shrinkers. We develop several estimates which are much sharper than their counterparts in…
Hecke modifications of Higgs bundles and the extended Bogomolny equation
Siqi He, Thomas Walpuski
We establish a Kobayashi-Hitchin correspondence between solutions of the extended Bogomolny equation with a Dirac type singularity and Hecke modifications of Higgs bundles. This co…
The Extended Bogomolny Equations and Generalized Nahm Pole Boundary Condition
Siqi He, Rafe Mazzeo
In this paper we develop a Kobayashi-Hitchin type correspondence between solutions of the extended Bogomolny equations on $Σ\times \RP$ with Nahm pole singularity at $Σ\times \{0\}…
Cohomogeneity-one -Laplacian flow on 7-torus
Hongnian Huang, Yuanqi Wang, Chengjian Yao
We prove the hypersymplectic flow of simple type on standard torus exists for all time and converges to the standard flat structure modulo diffeomorphisms. This resu…
A Gluing Theorem for the Kapustin-Witten Equations with a Nahm Pole
Siqi He
In the present paper, we establish a gluing construction for the Nahm pole solutions to the Kapustin-Witten equations over manifolds with boundaries and cylindrical ends. Given two…
Long-time existence for Yang-Mills flow
Alex Waldron
We establish that finite-time singularities do not occur in four-dimensional Yang-Mills flow, confirming the conjecture of Schlatter, Struwe, and Tahvildar-Zadeh. The proof relies…