6 citations · 27 across the 13 of their papers we have counts for
13 papers
The Algebraic and Analytic Compactifications of the Hitchin Moduli Space
Siqi He, Rafe Mazzeo, Xuesen Na +1
Following the work of Mazzeo-Swoboda-Weiss-Witt and Mochizuki, there is a map between the algebraic compactification of the Dolbeault moduli space of $\mathsf{SL}(2,\m…
Existence of nondegenerate harmonic 1-forms via symmetry
Siqi He
Using symmetry, we present a topological condition for the existence of the harmonic 1-forms over Riemannian manifold. As a corollary, if is an or…
The branched deformations of the special Lagrangian submanifolds
Siqi He
The branched deformations of immersed compact special Lagrangian submanifolds are studied in this paper. If there exists a nondegenerate harmonic 1-form over a speci…
On the Moduli Space of the Octonionic Nahm's Equations
Siqi He
In this paper, we study some basic properties of the octonionic Nahm's equations over . We prove that the moduli space of the smooth solutions to the octonionic Nahm's equat…
The behavior of sequences of solutions to the Hitchin-Simpson equations
Siqi He
The Hitchin-Simpson equations are first-order non-linear equations for a pair consisting of a connection and a Higgs field. In this paper, we study the behavior of sequences of sol…
Opers and the twisted Bogomolny equations
Siqi He, Rafe Mazzeo
In this paper, we study the dimensionally reduced twisted Kapustin-Witten equations on the product of a compact Riemann surface with . The main result is a Kobaya…
Classification of Nahm pole solutions of the Kapustin-Witten equations on
Siqi He, Rafe Mazzeo
In this note, we classify all solutions to the Kapustin-Witten equations on , where is a compact Riemann surface, with Nahm pole…
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 Expansions of the Nahm Pole Solutions to the Kapustin-Witten Equations
Siqi He
For a 3-manifold and compact simple Lie group , we study the expansions of polyhomogeneous Nahm pole solutions to the Kapustin-Witten equations over . L…
The extended Bogomolny equations with generalized Nahm pole boundary conditions, II
Siqi He, Rafe Mazzeo
We develop a Kobayashi-Hitchin correspondence for the extended Bogomolny equations, i.e., the dimensionally reduced Kapustin-Witten equations, on the product of a compact Riemann s…
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\}…
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…
Rotationally Invariant Singular Solutions to the Kapustin-Witten Equations
Siqi He
In the present paper, we find a system of non-linear ODEs that gives rotationally invariant solutions to the Kapustin-Witten equations in 4-dimensional Euclidean space. We explicit…