Invariant measures for actions of unipotent groups over local fields on homogeneous spaces

From MaRDI portal
Publication:1320053

DOI10.1007/BF01231565zbMath0816.22004OpenAlexW2088544526MaRDI QIDQ1320053

George Tomanov, Gregory A. Margulis

Publication date: 10 November 1994

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/144192




Related Items

Positive entropy invariant measures on the space of lattices with escape of massA special case of effective equidistribution with explicit constantsOn the density of S-adic integers near some projective G-varietiesAsymptotic distribution of values of isotropic here quadratic forms at \(S\)-integral pointsJoinings of higher-rank diagonalizable actions on locally homogeneous spacesFrom rational billiards to dynamics on moduli spacesRaghunathan's conjectures for Cartesian products of real and \(p\)-adic Lie groupsClassification of joinings for Kleinian groupsInvariant and stationary measures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli spaceA joinings classification and a special case of Raghunathan's conjecture in positive characteristic (with an appendix by Kevin Wortman)C1 actions on manifolds by lattices in Lie groupsValues of pairs involving one quadratic form and one linear form at \(S\)-integral pointsSuperrigidity for homomorphisms into isometry groups of \(\text{CAT}(-1)\) spacesDiagonal actions in positive characteristicHausdorff dimension of limit setsTowards an effective version of Mazur conjectureOn the dimension drop conjecture for diagonal flows on the space of latticesJoinings of higher rank torus actions on homogeneous spacesEscape of mass and entropy for diagonal flows in real rank one situationsMixing of frame flow for rank one locally symmetric spaces and measure classificationIntroduction to random walks on homogeneous spacesQuantitative disjointness of nilflows from horospherical flowsSmooth ergodic theory of \(\mathbb{Z}^d \)-actionsOn the density of some sparse horocyclesEffective equidistribution for multiplicative Diophantine approximation on linesStationary measures and invariant subsets of homogeneous spaces. II.Characters of algebraic groups over number fieldsDistribution of periodic torus orbits and Duke's theorem for cubic fieldsStationary measures and closed invariants on homogeneous spacesA tour through Mirzakhani’s work on moduli spaces of Riemann surfacesJoint equidistribution of CM pointsDistribution of shapes of orthogonal latticesSymmetry of entropy in higher rank diagonalizable actions and measure classificationValues of indefinite quadratic forms at integral points and flows on spaces of latticesEffective estimates on indefinite ternary formsMinimality and unique ergodicity of homogeneous actionsConvergence of measures under diagonal actions on homogeneous spacesOn unipotent flows in ℋ(1,1)Characteristic free measure rigidity for the action of solvable groups on homogeneous spacesLocal-global principles for representations of quadratic formsEntropy and escape of mass for SL\(_3(\mathbb{Z})\backslash\) SL\(_3 (\mathbb{R})\)Rational points on homogeneous varieties and equidistribution of adelic periods (with appendix by Mikhail Borovoi)Stationary measures and invariant subsets of homogeneous spaces (II)Linnik's problems and maximal entropy methodsAlmost-prime times in horospherical flows on the space of latticesJoining measures for horocycle flows on abelian coversInteger points on spheres and their orthogonal gridsThe case of equality in the dichotomy of Mohammadi-OhStationary measures and invariant subsets of homogeneous spacesTopological proof of Benoist-Quint's orbit closure theorem for \(\mathrm{SO}(d, 1) \)Closures of locally divergent orbits of maximal tori and values of homogeneous formsHausdorff dimension of divergent trajectories on homogeneous spacesEffective equidistribution and property (𝜏)Distribution of periodic torus orbits on homogeneous spacesEffective equidistribution for closed orbits of semisimple groups on homogeneous spacesLimiting distributions of translates of divergent diagonal orbitsEffectivity of uniqueness of the maximal entropy measure on -adic homogeneous spacesEquidistribution of expanding measures with local maximal dimension and Diophantine approximationBadly approximable points on manifolds and unipotent orbits in homogeneous spacesParabolic perturbations of unipotent flows on compact quotients of \(\mathrm{SL}(3,\mathbb{R})\)Measure rigidity for almost linear groups and its applicationsHow far are \(p\)-adic Lie groups from algebraic groups?Arithmeticity of discrete subgroups containing horospherical latticesThe work of Einsiedler, Katok and Lindenstrauss on the Littlewood conjectureArithmeticity of discrete subgroupsInvariant measures and measurable projective factors for actions of higher-rank lattices on manifoldsEquidistribution in \(S\)-arithmetic and adelic spacesInvariant Radon measures for Unipotent flows and products of Kleinian groupsOn measures invariant under tori on quotients of semisimple groupsRigidity of multiparameter actionsRigidity of measures -- the high entropy case and non-commuting foliations



Cites Work