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

Loewner driving functions encode simple curves in 2-dimensional simplyconnected domains by real-valued functions. We prove that the Loewner drivingfunction of a $C^{1,\beta}$ curve (differentiable parametrization with$\beta$-H\"older continuous derivative) is in the class $C^{1,\beta-1/2}$ if$1/2<\beta\leq 1$, and in the class $C^{0,\beta + 1/2}$ if $0 \leq \beta \leq1/2$. This is the converse of a result of Carto Wong and is optimal. We alsointroduce the Loewner energy of a rooted planar loop and use our regularityresult to show the independence of this energy from the basepoint.

The Loewner energy of loops and regularity of driving functions