关于 $(4,6)$ 型胖分布中圆盘的水平浸入

Fat分布中水平浸入的存在性

Existence of Horizontal Immersions in Fat Distributions

本文为余秩2的fat分布定义了数值不变量“度”，并利用Gromov的h-原理技术证明了任意流形到度为2的fat分布及四元数接触结构中水平浸入的存在性。

球面的等距浸入与浸没中的胖赤道效应与极小性

Fat equator effect and Minimality in immersions and submersions of the Sphere

本文受球面赤道测度集中现象启发，刻画了闭等距极小浸入与极小黎曼浸没所满足的赤道测度集中性质。

Biminimal immersions

We study biminimal immersions, that is immersions which are critical points of the bienergy for normal variations with fixed energy. We give a geometrical description of the Euler-Lagrange equation associated to biminimal immersions for: i) biminimal curves in a Riemannian manifold, with particular care to the case of curves in a space form ii) isometric immersions of codimension one in a Riemannian manifold, in particular for surfaces of a three-dimensional manifold. We describe two methods to construct families of biminimal surfaces using both Riemannian and horizontally homothetic submersio…

最优质量传输的和乐：光滑情形

The Holonomy of Optimal Mass Transport: The Smooth Case

在无边界光滑n维黎曼流形上，证明任意向量场可表示为至多max{6,6n−3}个梯度向量场对的深度1李括号的线性组合，结合强Trotter性质，得到紧致连通流形上微分同胚型最优传输映射生成的群在微分同胚群恒等分支中稠密的结论。

Classification of tangent and transverse knots in bracket-generating distributions

Consider a manifold, of dimension greater than 3, equipped with a bracket-generating distribution. In this article we prove complete h-principles for embedded regular horizontal curves and for embedded transverse curves. These results contrast with the 3-dimensional contact case, where the full h-principle for transverse/legendrian knots is known not to hold. We also prove analogous statements for immersions, with no assumptions on the ambient dimension.