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

Our main result marks progress on an old conjecture of Vitushkin. We showthat a compact set in the plane with plenty of big projections (PBP) haspositive analytic capacity, along with a quantitative lower bound. A higherdimensional counterpart is also proved for capacities related to the Rieszkernel, including the Lipschitz harmonic capacity. The proof uses aconstruction of a doubling Frostman measure on a lower content regular set,which may be of independent interest. Our second main result is the Analyst'sTraveling Salesman Theorem for sets with plenty of big projections. As acorollary, we obtain a lower bound for the Hausdorff dimension of uniformlywiggly sets with PBP. The second corollary is an estimate for the capacities ofsubsets of sets with PBP, in the spirit of the quantitative solution toDenjoy's conjecture.

Analytic capacity and dimension of sets with plenty of big projections