Completeness of projective special Kähler and quaternionic Kähler manifolds

四元数叶状结构与orbifolds的上同调

Cohomology of Quaternionic Foliations and Orbifolds

研究四元数叶状结构与orbifolds的上同调，先回顾四元数几何等定义横向四元数凯勒叶状结构，证明相关经典结果的叶状版本，最后为四元数orbifolds重新阐述结果。

Completeness in supergravity constructions

We prove that the supergravity r- and c-maps preserve completeness. As a consequence, any component H of a hypersurface {h=1} defined by a homogeneous cubic polynomial such that -d^2 h is a complete Riemannian metric on H defines a complete projective special Kahler manifold and any complete projective special Kahler manifold defines a complete quaternionic Kahler manifold of negative scalar curvature. We classify all complete quaternionic Kahler manifolds of dimension less or equal to 12 which are obtained in this way and describe some complete examples in 16 dimensions.

超埃尔米特流形上四元数蒙日-安培方程的精确一致界

Sharp uniform bound for the quaternionic Monge-Ampere equation on hyperhermitian manifolds

本文利用Guo和Phong的最新方法，为超埃尔米特流形上的四元数蒙日-安培方程及一系列相关四元数偏微分方程提供了精确的 $C^0$ 一致估计，改进了先前对右端范数和初始度量条件的依赖。