Extremal Affine Subspaces and Khintchine-Jarník Type Theorems

• Published in: Geometric and functional analysis Vol. 34; no. 1; pp. 113 - 163
• Main Author: Huang, Jing-Jing
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.02.2024; Springer Nature B.V
• Subjects: Analysis; Classification; Mathematics; Mathematics and Statistics; Subspaces; Theorems; 11J83; 11J13; 11P21

We prove a conjecture of Kleinbock which gives a clear-cut classification of all extremal affine subspaces of . We also give an essentially complete classification of all Khintchine type affine subspaces, except for some boundary cases within two logarithmic scales. More general Jarník type theorems...