For Gromov-Piatetski-Shapiro hybrid hyperbolic n-manifolds, the number of codimension-one totally geodesic hyperplanes is bounded by an explicit (if weak) function of volume and dynamical constants.
Effective equidistribution of large dimensional measures on affine invariant submanifolds
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
The unstable foliation, that locally is given by changing horizontal components of period coordinates, plays an important role in study of translation surfaces, including their deformation theory and in the understanding of horocycle invariant measures. In this article we show that measures of large dimension on the unstable foliation equidistribute in affine invariant submanifolds and give an effective rate. An analogous result in the setting of homogeneous dynamics is crucially used in the effective density and equidistribution results of Lindenstrauss-Mohammadi and Lindenstrauss--Mohammadi--Wang.
fields
math.DS 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Quantitative finiteness of hyperplanes in hybrid manifolds
For Gromov-Piatetski-Shapiro hybrid hyperbolic n-manifolds, the number of codimension-one totally geodesic hyperplanes is bounded by an explicit (if weak) function of volume and dynamical constants.