Multiplicative Diophantine exponents of hyperplanes and their nondegenerate submanifolds
Yuqing Zhang
TL;DR
This paper investigates how multiplicative Diophantine exponents of hyperplanes are preserved in their nondegenerate submanifolds using multiparameter dynamics and quantitative nondivergence techniques.
Contribution
It establishes that the multiplicative Diophantine exponents of hyperplanes are inherited by their nondegenerate submanifolds, advancing understanding in Diophantine approximation.
Findings
Multiplicative Diophantine exponents are inherited by nondegenerate submanifolds.
Uses multiparameter dynamics and quantitative nondivergence methods.
Provides new insights into Diophantine properties of submanifolds.
Abstract
We consider multiparameter dynamics on the space of unimolular lattices. Along with quantitative nondivergence we prove that multiplicative Diophantine exponents of hyperplanes are inherited by their nondegenerate submanifolds.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Topological and Geometric Data Analysis · Geometry and complex manifolds