Dirichlet principal eigenvalue comparison theorems in geometry with torsion
Abstract
We describe min-max formulas for the principal eigenvalue of a -drift Laplacian defined by a vector field on a geodesic ball of a Riemannian manifold . Then we derive comparison results for the principal eigenvalue with the one of a spherically symmetric model space endowed with a radial vector field, under pointwise comparison of the corresponding radial sectional and Ricci curvatures, and of the radial component of the vector fields. These results generalize the known case .
Cite
@article{arxiv.1509.01967,
title = {Dirichlet principal eigenvalue comparison theorems in geometry with torsion},
author = {Ana Cristina Ferreira and Isabel Salavessa},
journal= {arXiv preprint arXiv:1509.01967},
year = {2017}
}
Comments
Latex, 31 pages. The results of this paper were partially reported at the AMS-EMS-SPM international meeting at Porto, 10-13 June 2015. V3. We add a detailed description of the entire spectrum of the H-Laplacian on a geodesic ball of a model space. Accepted for publication in the Journal of Mathematical Analysis and Applications ( 13/04/2017)