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 prove that if M is a closed 4-dimensional Riemannian manifold with trivial first homology group, Ricci curvature $$|Ric|\le 3$$ | R i c | ≤ 3 , diameter $${{\,\mathrm{diam}\,}}(M)\le D$$ diam ( M ) ≤ D , and volume $${{\,\mathrm{vol}\,}}(M)>v>0$$ vol ( M ) > v > 0 , then the smallest area of a 2-dimensional minimal surface in M is bounded by F ( v ,  D ), for some function F that only depends on v and D . In order to prove this result, we first establish upper bounds for the first homological filling function of M that are of independent interest. This part of our work is based on recent results of Cheeger and Naber about manifolds with Ricci curvature bounded from both sides.

An Upper Bound for the Smallest Area of a Minimal Surface in Manifolds of Dimension Four