Zobrazeno 1 - 10
of 177
pro vyhledávání: '"He, Weiyong"'
A hypersymplectic structure on a 4-manifold is a triple $\omega_1, \omega_2, \omega_3$ of 2-forms for which every non-trivial linear combination $a^1\omega_1 + a^2 \omega_2 + a^3 \omega_3$ is a symplectic form. Donaldson has conjectured that when the
Externí odkaz:
http://arxiv.org/abs/2404.15016
Autor:
He, Weiyong
Given a symplectic class $[\omega]$ on a four torus $T^4$ (or a $K3$ surface), a folklore problem in symplectic geometry is whether symplectic forms in $[\omega]$ are isotropic to each other. We introduce a family of nonlinear Hodge heat flows on com
Externí odkaz:
http://arxiv.org/abs/2310.03651
The aim of this article is to study the residual Monge-Amp\`{e}re mass of a plurisubharmonic function with an isolated singularity, provided with the circular symmetry. With the aid of Sasakian geometry, we obtain an estimate on the residual mass of
Externí odkaz:
http://arxiv.org/abs/2309.13288
Autor:
He, Weiyong
We introduce the notion of \emph{biharmonic almost complex structure} on a compact almost Hermitian manifold and we study its regularity and existence in dimension four. First we show that there always exist smooth energy-minimizing biharmonic almost
Externí odkaz:
http://arxiv.org/abs/2006.05958
We prove that for any two closed Riemannian manifolds $M^{2m}$ ($m\geq 1$) and $N$, there exists a minimizing (extrinsic) $m$-polyharmonic map for every free homotopy class in $[M^{2m}, N]$, provided that the homotopy group $\pi_{2m}(N)$ is trivial.
Externí odkaz:
http://arxiv.org/abs/1911.00849
Publikováno v:
In Journal of Functional Analysis 1 September 2023 285(5)
Autor:
He, Weiyong, Jiang, Ruiqi
In this paper we consider the existence and regularity of weakly polyharmonic almost complex structures on a compact almost Hermitian manifold $M^{2m}$. Such objects satisfy the elliptic system weakly $[J, \Delta^m J]=0$. We prove a very general regu
Externí odkaz:
http://arxiv.org/abs/1909.09959
The Gursky-Streets equation are introduced as the geodesic equation of a metric structure in conformal geometry. This geometric structure has played a substantial role in the proof of uniqueness of $\sigma_2$ Yamabe problem in dimension four. In this
Externí odkaz:
http://arxiv.org/abs/1907.12313
Autor:
He, Weiyong, Li, Bo
We define and study the harmonic heat flow for almost complex structures which are compatible with a Riemannian structure $(M, g)$. This is a tensor-valued version of harmonic map heat flow. We prove that if the initial almost complex structure $J$ h
Externí odkaz:
http://arxiv.org/abs/1907.12210
Autor:
He, Weiyong
We study the existence and regularity of energy-minimizing harmonic almost complex structures. We have proved results similar to the theory of harmonic maps, notably the classical results of Schoen-Uhlenbeck and recent advance by Cheeger-Naber.
Externí odkaz:
http://arxiv.org/abs/1907.12211