Complex Scaling and Geometric Analysis of Several Variables

Constructing soliton solutions of geometric flows by separation of variables

This note surveys and compares results on the separation of variables construction for soliton solutions of curvature equations including the Kähler-Ricci flow and the Lagrangian mean curvature flow. In the last section, we propose some new generalizations in the Lagrangian mean curvature flow case.

Life-span of classical solutions to hyperbolic geometric flow in two space variables with slow decay initial data

In this paper we investigate the life-span of classical solutions to the hyperbolic geometric flow in two space variables with slow decay initial data. By establishing some new estimates on the solutions of linear wave equations in two space variables, we give a lower bound of the life-span of classical solutions to the hyperbolic geometric flow with asymptotic flat initial Riemann surfaces.

几何墙壁：流形结构预测逐层稀疏自编码器扩展定律

The Geometric Wall: Manifold Structure Predicts Layerwise Sparse Autoencoder Scaling Laws

本文研究稀疏自编码器中逐层扩展定律的几何原因，发现流形结构决定了每层宽度指数，且跨模型转移表明存在可传递的几何定律。