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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let (M,g) be a compact, connected riemannian manifold that is homogeneous,i.e. each pair of points p,q in M have isometric neighborhoods. This paper is afirst step towards an understanding of the extent to which it is true that foreach "generic" initial condition f0, the solution to the Heat Equation is suchthat for sufficiently large t, f(.,t) is a minimal Morse function, i.e., aMorse function whose total number of critical points is the minimal possible onM. In this paper we show that this is true for flat tori and round spheres inall dimensions.

A remark on the Heat Equation and minimal Morse Functions on Tori and Spheres