arXiv subjects

Xinan Ma

Publications and source records attributed to Xinan Ma.

2 recordsLinked to original sources

arXiv2021

Entire solutions of the magnetic Ginzburg-Landau equation in $\mathbb{R}^4$

We construct entire solutions of the magnetic Ginzburg-Landau equations in dimension 4 using Lyapunov-Schmidt reduction. The zero set of these solutions are close to the minimal submanifolds studied by Arezzo-Pacard\cite{Arezzo}. We also show the existence of a saddle type solution to the equations, whose zero set consists of two vertical planes in $\mathbb{R}^4$. These two types of solutions are believed to be energy minimizers of the corresponding energy functional and lie in the same connect component of the moduli space of entire solutions.

math.AP↗

arXiv2010

On a class of fully nonlinear flow in Kähler geometry

In this paper, we study a class of fully nonlinear metric flow on Kähler manifolds, which includes the J-flow as a special case. We provide a sufficient and necessary condition for the long time convergence of the flow, generalizing the result of Song-Weinkove. As a consequence, under the given condition, we solved the corresponding Euler equation, which is fully nonlinear of Monge-Ampère type. As an application, we also discuss a complex Monge-Ampère type equation including terms of mixed degrees, which was first posed by Chen.

math.DG↗