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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We prove the existence of a continuous $BV$ minimizer with $C^{0}$ boundaryvalue for the $p$-area (pseudohermitian or horizontal area) in a parabolicallyconvex bounded domain. We extend the domain of the area functional from $BV$functions to vector-valued measures. Our main purpose is to study the first andsecond variations of such a generalized area functional including thecontribution of the singular part. By giving examples in Riemannian andpseudohermitian geometries, we illustrate several known results in a unifiedway. We show the contribution of the singular curve in the first and secondvariations of the $p$-area for a surface in an arbitrary pseudohermitian$3$-manifold.

Variations of generalized area functionals and p-area minimizers of bounded variation in the Heisenberg group