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, free boundary geodesic networks whose length realize the firstmin-max width of the length functional are investigated. This functional actson the space of relative flat 1-dimensional cycles modulo 2 in a compactsurface with boundary. The widths are special critical values of the volumefunctional in some class of submanifolds which naturally arise in the Min-maxTheory of Almgren and Pitts.  The main result of this work concerns the existence of a geodesic networkwith a rather simple structure which realizes the first width of a surface withnon-negative sectional curvature and strictly convex boundary. More precisely,it is either a simple geodesic meeting the boundary orthogonally, or a geodesicloop with vertex at a boundary point determining two equal angles with thatboundary curve.

The first width of non-negatively curved surfaces with convex boundary