Proof of the gradient conjecture of R.!Thom

• 成果类型: Article
• 署名作者: Kurdyka, K; Mostowski, T; Parusinski, A
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/2661354
• 发表日期: 2000
• 页码: 763-792
• 关键词: STRATIFICATION; sets

摘要

Let x(t) be a trajectory of the gradient of a real analytic function and suppose that to is a limit point of x(t). We prove the gradient conjecture of R. Them which states that the secants of x(t) at to have a limit. Actually we show a stronger statement: the radial projection of x(t) from to onto the unit sphere has finite length.