Small-time asymptotics of hypoelliptic heat kernels near the diagonal, nilpotentization and related results
From MaRDI portal
Publication:2077179
DOI10.5802/ahl.93zbMath1484.35159arXiv2004.06461OpenAlexW3199328001MaRDI QIDQ2077179
Luc Hillairet, Yves Colin de Verdière, Emmanuel Trélat
Publication date: 24 February 2022
Published in: Annales Henri Lebesgue (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2004.06461
Singular perturbations in context of PDEs (35B25) Hypoelliptic equations (35H10) Sub-Riemannian geometry (53C17) Subelliptic equations (35H20) Heat kernel (35K08)
Related Items (5)
Trivializable and quaternionic subriemannian structures on \({\mathbb{S}}^7\) and subelliptic heat kernel ⋮ Spectral summability for the quartic oscillator with applications to the Engel group ⋮ Spectral estimates and asymptotics for stratified Lie groups ⋮ Weyl's law for singular Riemannian manifolds ⋮ Cartan connections for stochastic developments on sub-Riemannian manifolds
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Quantum ergodicity and quantum limits for sub-Riemannian Laplacians
- On the Hausdorff volume in sub-Riemannian geometry
- Small time Gaussian estimates of heat diffusion kernels. II: The theory of large deviations
- Perturbations singulières dans les problèmes aux limites et en contrôle optimal
- Décroissance exponentielle du noyau de la chaleur sur la diagonale. I. (Exponential decay of the heat kernel over the diagonal. I)
- Exponential decay of the heat kernel over the diagonal. II
- Classification of Carnot algebras: the semi-rigid cases
- Long time estimates for the heat kernel associated with a uniformly subelliptic symmetric second order operator
- The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups
- Semigroups of linear operators and applications to partial differential equations
- Fundamental solutions and geometry of the sum of squares of vector fields
- Collapsing of Riemannian manifolds and eigenvalues of Laplace operator
- The wave equation for a hypoelliptic operator with symplectic characteristics of codimension two
- Sub-Riemannian geometry
- Asymptotic expansion of the hypoelliptic heat kernel on the diagonal
- Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
- On the eigenvalues of a class of hypoelliptic operators
- Estimations of the heat kernel on homogeneous spaces
- Spectral properties of hypoelliptic operators
- Sub-Riemannian limit of the differential form spectrum of contact manifolds
- Spectral asymptotics for sub-Riemannian Laplacians. I: Quantum ergodicity and quantum limits in the 3-dimensional contact case
- Hypoelliptic estimates and spectral theory for Fokker-Planck operators and Witten Laplacians
- Phénomènes de perturbation singulière dans les problèmes aux limites
- On the division of distributions by polynomials
- Trace heat kernel asymptotics in 3D contact sub-Riemannian geometry
- Rigid Carnot algebras: a classification
- Hypoelliptic second order differential equations
- Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérées
- Fonction spectrale et valeurs propres d'une classe d'operateurs non elliptiques
- Off diagonal short time asymptotics for fundamental solution of diffusion equation
- One-Parameter Semigroups for Linear Evolution Equations
- Collapsing Riemannian Metrics to Carnot-Caratheodory Metrics and Laplacians to Sub-Laplacians
- On the Principle of not Feeling the Boundary for Diffusion Processes
- A Comprehensive Introduction to Sub-Riemannian Geometry
- Sub-Riemannian Geometry and Optimal Transport
- Gaussian heat kernel upper bounds via the Phragmén-Lindelöf theorem
- Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning
This page was built for publication: Small-time asymptotics of hypoelliptic heat kernels near the diagonal, nilpotentization and related results