Flows on S-arithmetic homogeneous spaces and applications to metric Diophantine approximation
By Dmitry Kleinbock, G. Tomanov. 2005
112 citations recorded by the source corpus.
The main goal of this work is to establish quantitative nondivergence estimates for flows on homogeneous spaces of products of real and p-adic Lie groups. These results have applications both to ergodic theory and to Diophantine approximation. Namely, earlier results of Dani (finiteness of locally finite ergodic unipotent-invariant measures on real homogeneous spaces) and Kleinbock?Margulis (strong extremality of nondegenerate submanifolds of Rn) are generalized to the S-arithmetic setting.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ace59f9da28cdbbf435555e381a0e6f825d43664
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In Geometry and Topology
- Dmitry Kleinbock
- Elon Lindenstrauss
- Victor Beresnevich
- Barak Weiss
- Yann Bugeaud
- Manfred Einsiedler
- Sanju Velani
- Lior Fishman
In Mathematical Physics
- Dmitry Kleinbock
- Victor Beresnevich
- Barak Weiss
- Elon Lindenstrauss
- Yann Bugeaud
- Lior Fishman
- Manfred Einsiedler
- Sanju Velani
Citations in the corpus
- Rational points near manifolds and metric Diophantine approximation (2009, background): “The work of Kleinbock and Margulis has also dealt with the far more delicate multiplicative case known as the Baker-Sprindžuk conjecture and led to a surge of activity that led to establishing the extremality of various classes of manifolds and sets; see, for example, [38], [39], [40], [42].”
- On fractal measures and diophantine approximation (2005, background): “The recent preprint [ KT ] by G. Tomanov and the first named author contains more details.”