In this note, using the Kendall-Cranston coupling, we study on Kähler (resp. quaternion Kähler) manifolds first eigenvalue estimates in terms of dimension, diameter, and lower bounds on the holomorphic (resp. quaternionic) sectional curvature.
Fabrice Baudoin and Guang Yang were supported in part by National Science Foundation grant DMS-1901315.
"A note on first eigenvalue estimates by coupling methods in Kähler and quaternion Kähler manifolds." Electron. Commun. Probab. 27 1 - 8, 2022. https://doi.org/10.1214/22-ECP452