English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let $(M,\theta)$ be a compact strictly pseudoconvex pseudohermitian manifoldwhich is CR embedded into a complex space. In an earlier paper, Lin and theauthors gave several sharp upper bounds for the first positive eigenvalue$\lambda_1$ of the Kohn-Laplacian $\Box_b$ on $(M,\theta)$. In the presentpaper, we give a sharp upper bound for $\lambda_1$, generalizing and extendingsome previous results. As a corollary, we obtain a Reilly-type estimate when$M$ is embedded into the standard sphere. In another direction, using aLichnerowicz-type estimate by Chanillo, Chiu, and Yang and an explicit formulafor the Webster scalar curvature, we give a lower bound for $\lambda_1$ whenthe pseudohermitian structure $\theta$ is volume-normalized.

The Webster scalar curvature and sharp upper and lower bounds for the first positive eigenvalue of the Kohn-Laplacian on real hypersurfaces