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Equidistribution of Expanding Translates of Curves in homogeneous spaces with the Action of(SO(n,1))^(k)

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Acta Mathematica Sinica,English Series 2022年第1期38卷 205-224页

作者： Lei YANG College of Mathematics Sichuan UniversityChengdu 610000P.R.China

Let X=G/Γbe a homogeneous space with ambient group G containing the group H=(SO(n,1))^(k)and x∈X be such that Hx is dense in *** an analytic curve?:I=[a,b]→H,we will show that ifφsatisfies certain geometric condition,then for a typical diagonal subgroup A={a(t):t∈R}■H the translates{a(t)?(I)x:t>0}of the curve?(I)x will tend to be equidistributed in X as t→+∞.The proof is based on Ratner's theorem and linearization technique.

关键词： Equidistribution homogeneous spaces Ratner's theorem

Boundedness of Linear Commutators on Herz-Morrey spaces on spaces of homogeneous Type

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Chinese Quarterly Journal of Mathematics 2010年第2期25卷 172-181页

作者： GAO Wen-hua JIANG Yin-sheng GONG Xiao-bing College of Mathematics and System Science Xinjiang University Urumqi 830046 China College of Mathematics and Information Science Neijiang Normal University Neijiang 641112 China

Under certain weak local size conditions, the boundedness of linear commutators on Herz-Morrey spaces on spaces of homogeneous type are studied. In addition, the boundedness of Hardy-Littlewood maximum commutators on ... 详细信息

关键词： homogeneous spaces Herz spaces commutators Hardy-Littlewood maximum function

Harmonic Analysis for Real Spherical spaces

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Acta Mathematica Sinica,English Series 2018年第3期34卷 341-370页

作者： Bernhard KROTZ Henrik SCHLICHTKRULL Universitat Paderborn Institut fiir MathematikWarburger Strafle 10033098 PaderbornGermany University of Copenhagen Department of MathematicsUniversitetsparken 5DK-2100 Copenhagen ODenmark

We give an introduction to basic harmonic analysis and representation theory for homogeneous spaces Z = G/H attached to a real reductive Lie group G. A special emphasis is made to the case where Z is real spherical.

关键词： Real spherical spaces harmonic analysis homogeneous spaces representation theory

Poisson Matrices on 3-Manifolds and Their Applications to 3-CPM Manifolds

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Acta Mathematica Sinica,English Series 2001年第4期17卷 697-714页

作者： Hong Jun LI Science School. Xi’an Jiaotong University, Xi’an 710049, P. R. China Science School Xi'an Jiaotong University Xi'an 710049 P. R. China

In this paper, the existence of a global tangent frame on every oriented and connected smooth 3-manifold will be used to develop a global frame method in 3-dimensional geometry and topology. Corresponding to each global tangent frame, we define a Poisson matrix on the 3-manifold. And using it as an initial date. we give an explicit expression of all the curvatures for some Riemannian metric. The method is well applied to 3-manifolds with constant Poisson matrix. Such 3-manifolds are essentially the homogeneous spaces of 3-dimensional Lie groups.

关键词： Global frames Poisson matrix Curvature 3-CPM manifolds homogeneous spaces

Geometric Counting on Wavefront Real Spherical spaces

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Acta Mathematica Sinica,English Series 2018年第3期34卷 488-531页

作者： Bernhard KROTZ Eitan SAYAG Henrik SCHLICHTKRULL Universitat Paderborn Institut Jur MathematikWarburger Strafle 10033098 PaderbornDeutschland Department of Mathematics Ben Gurion University of the NegevP.O.B.653Be'er Sheva 84105Israel Department of Mathematics University of CopenhagenUniversitetsparken 5DK-2100 Copenhagen ODenmark

We provide L^p-versus L~∞-bounds for eigenfunctions on a real spherical space Z of wavefront type. It is shown that these bounds imply a non-trivial error term estimate for lattice counting on Z. The paper also serve... 详细信息

关键词： homogeneous spaces real spherical spaces lattice counting error term wavefront lemma spectral analysis norm comparison of eigenfunctions

Almost nonnegative curvature operator and cohomology rings

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Frontiers of Mathematics in China 2016年第5期11卷 1259-1274页

作者： Martin HERRMANN Fakultat fur Mathematik Karlsruher Institut fur Technologie Kaiserstraβe 89-93 76133 Karlsruhe Germany

We give a survey of results on the construction of and obstructions to metrics of almost nonnegative curvature operator on closed manifolds and results on the cohomology rings of closed, simply-connected manifolds with a lower curvature and upper diameter bound. The latter is motivated by a question of Grove whether these condition imply finiteness of rational homotopy types. This question has answers by F. Fang-X. Rong, B. Totaro and recently A. Dessai and the present author.

关键词： Nonnegative curvature homogeneous spaces curvature operator almost nonnegative curvature