数学研究所
学术报告
偏微分方程研讨班
Speaker: 苏治铜 讲师（湖南师范大学）
Inviter: 邱国寰 副研究员
Language: Chinese
Title: A decomposition lemma in convex integration via classical algebraic geometry
Time&Venue: 2025年6月4日（星期三）10:00-11:00
&晨兴410
Abstract:In this talk, we introduce a decomposition lemma in the convex integration scheme. The lemma allows error terms to be expressed using fewer rank-one symmetric matrices than n(n+1)/2 within constructing flexible C^(1,α) solutions to a system of nonlinear PDEs in dimension n ≥ 2, which can be viewed as a kind of truncation of the codimension one local isometric embedding equation in Nash-Kuiper Theorem. This leads to flexible solutions with higher Holder regularity, and consequently, improved very weak solutions to certain geometric equations. Our arguments involve applications of several results from algebraic geometry and topology, including theorem on vector fields on spheres, the intersection of projective varieties, and projective duality. We also use an elliptic method ingeniously that avoids loss of differentiability. Consequently, our improvement on exponent involves the Radon-Hurwitz number, which exhibits an 8-fold periodicity on n that is related to Bott periodicity.This is a joint work with Weijun Zhang.
