A LICHNEROWICZ ESTIMATE FOR THE SPECTRAL GAP OF A SUB-LAPLACIAN

被引：1

作者：

Berge, Stine Marie ^{[1
]}

Grong, Erlend ^{[2
,3
]}

机构：

[1] Norwegian Univ Sci & Technol, Dept Math Sci, N-7491 Trondheim, Norway

[2] Univ Paris Saclay, Univ Paris Sud, Lab Signaux & Syst L2S Supelec, CNRS, 3 Rue Joliot Curie, F-91192 Gif Sur Yvette, France

[3] Univ Bergen, Dept Math, POB 7803, N-5020 Bergen, Norway

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 147卷 / 12期

关键词：

Spectral gap; Lichnerowicz estimate; sub-Laplacian; RIEMANNIAN MANIFOLDS; 1ST EIGENVALUE; INEQUALITIES; POINCARE; SOBOLEV; THEOREM;

D O I：

10.1090/proc/14223

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a second order operator on a compact manifold satisfying the strong Hormander condition, we give a bound for the spectral gap analogous to the Lichnerowicz estimate for the Laplacian of a Riemannian manifold. We consider a wide class of such operators which includes horizontal lifts of the Laplacian on Riemannian submersions with minimal leaves.

引用

收藏

页码：5153 / 5166

页数：14

相关论文

共 14 条

[1] The Lichnerowicz-Obata Theorem on Sub-Riemannian Manifolds with Transverse Symmetries [J].

Baudoin, Fabrice ;

Kim, Bumsik .

JOURNAL OF GEOMETRIC ANALYSIS, 2016, 26 (01) :156-170

[2] Sobolev, Poincare, and isoperimetric inequalities for subelliptic diffusion operators satisfying a generalized curvature dimension inequality [J].

Baudoin, Fabrice ;

Kim, Bumsik .

REVISTA MATEMATICA IBEROAMERICANA, 2014, 30 (01) :109-131

[3] Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality [J].

Baudoin, Fabrice ;

Bonnefont, Michel .

JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 262 (06) :2646-2676

[4]

Fefferman C., 1983, WADSWORTH MATH SER, VI, P590

[5] THE 1ST EIGENVALUE OF A SUBLAPLACIAN ON A PSEUDOHERMITIAN MANIFOLD [J].

GREENLEAF, A .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1985, 10 (02) :191-217

[6] Stochastic Completeness and Gradient Representations for Sub-Riemannian Manifolds [J].

Grong, Erlend ;

Thalmaier, Anton .

POTENTIAL ANALYSIS, 2019, 51 (02) :219-254

[7] Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: part I [J].

Grong, Erlend ;

Thalmaier, Anton .

MATHEMATISCHE ZEITSCHRIFT, 2016, 282 (1-2) :99-130

[8]

Grong E, 2016, MATH Z, V282, P131, DOI 10.1007/s00209-015-1535-3

[9] HYPOELLIPTIC 2ND ORDER DIFFERENTIAL EQUATIONS [J].

HORMANDE.L .

ACTA MATHEMATICA UPPSALA, 1967, 119 (3-4) :147-&

[10] The Sharp Lower Bound of the First Eigenvalue of the Sub-Laplacian on a Quaternionic Contact Manifold [J].

Ivanov, S. ;

Petkov, A. ;

Vassilev, D. .

JOURNAL OF GEOMETRIC ANALYSIS, 2014, 24 (02) :756-778