arXiv research

Study classifies solutions to specific equations on half-space and ball.

Extends soliton theory to non-compact cases.

New operators for $Q$-curvature on 5D pseudohermitian manifolds.

We prove that the higher harmonic signature of an even dimensional oriented Riemannian foliation of a compact Riemannian manifold with coefficients in a leafwise U(p,q)-flat complex bundle is a leafwise homotopy invariant. We also prove the leafwise homotopy invariance of the twisted higher Betti classes. Consequences …

Let $M^{2n-1}$ be the smooth boundary of a bounded strongly pseudo-convex domain $Ω$ in a complete Stein manifold $V^{2n}$. Then (1) For $n \ge 3$, $M^{2n-1}$ admits a pseudo-Eistein metric; (2) For $n \ge 2$, $M^{2n-1}$ admits a Fefferman metric of zero CR Q-curvature; and (3) for a compact strictly pseudoconvex CR em…

The study bounds Hausdorff measure of flat singular points in area-minimizing currents.

Study on curvature flow in 4D ball, proving existence and convergence.

In this article, we investigate deformation problems of $Q$-curvature on closed Riemannian manifolds. One of the most crucial notions we use is the $Q$-singular space, which was introduced by Chang-Gursky-Yang during 1990's. Inspired by the early work of Fischer-Marsden, we derived several results about geometry relate…

An old theorem of Weil and Kodaira says that for a compact Kähler manifold $X$ there is a closed logarithmic $1$-form with residue divisor $D$ if and only if $D$ is homologous to zero in $H_{2n-2}(X,\mathbb C)$. In the first part of this paper, we generalize the above theorem to general compact complex manifolds by sho…