Effective equidistribution of translates of large submanifolds in semisimple homogeneous spaces

Abstract

Let $G=S{L}_2(\mathbb{R}{)}^d$ and $\Gamma ={\Gamma }_0^d$ with ${\Gamma }_0$ a lattice in $S{L}_2(\mathbb{R})$. Let $S$ be any "curved" submanifold of small codimension of a maximal horospherical subgroup of $G$ relative to an $\mathbb{R}$-diagonalizable element $a$ in the diagonal of $G$. Then for $S$ compact our result can be described by saying that $a^n{\text{vol}}_S$ converges in an effective way to the volume measure of $G/\Gamma$ when $n\to \infty$, with ${\text{vol}}_S$ the volume measure on $S$.

35 pages. A minor error in the paper (concerning the definition of mixing function and the proof of Proposition 3.5) has been fixed. Some small changes made in light of comments from the referee

References in corpus (1)

• Sparse equidistribution problems, period bounds, and subconvexity

Cited by in corpus (2)

• Effective equidistribution of horocycle lifts
• Applications of joinings to sparse equidistribution problems