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

In this paper, we introduce a new combinatorial curvature on triangulatedsurfaces with inversive distance circle packing metrics. Then we prove thatthis combinatorial curvature has global rigidity. To study the Yamabe problemof the new curvature, we introduce a combinatorial Ricci flow, along which thecurvature evolves almost in the same way as that of scalar curvature along thesurface Ricci flow obtained by Hamilton \cite{Ham1}. Then we study the longtime behavior of the combinatorial Ricci flow and obtain that the existence ofa constant curvature metric is equivalent to the convergence of the flow ontriangulated surfaces with nonpositive Euler number. We further generalize thecombinatorial curvature to $\alpha$-curvature and prove that it is alsoglobally rigid, which is in fact a generalized Bower-Stephenson conjecture\cite{BS}. We also use the combinatorial Ricci flow to study the corresponding$\alpha$-Yamabe problem.

On a combinatorial curvature for surfaces with inversive distance circle packing metrics