Hausdorff dimensions of very well intrinsically approximable subsets of quadratic hypersurfaces

TL;DR

This paper establishes an upper bound on the Hausdorff dimension of very well intrinsically approximable points on quadratic hypersurfaces, extending previous results and utilizing advanced approximation frameworks.

Contribution

It provides a new upper bound on Hausdorff dimensions for specific intrinsic approximation sets on quadratic hypersurfaces, building on and extending prior theoretical frameworks.

Findings

Upper bound on Hausdorff dimension established

Extension of Pollington and Velani's theorem to quadratic hypersurfaces

Incorporation of advanced intrinsic approximation techniques

Abstract

We prove an analogue of a theorem of A. Pollington and S. Velani ('05), furnishing an upper bound on the Hausdorff dimension of certain subsets of the set of very well intrinsically approximable points on a quadratic hypersurface. The proof incorporates the framework of intrinsic approximation on such hypersurfaces first developed in the authors' joint work with D. Kleinbock (preprint '14) with ideas from work of D. Kleinbock, E. Lindenstrauss, and B. Weiss ('04).