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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Local conditions on boundaries of $C^\infty$ Levi-flat hypersurfaces, in casethe boundary is a generic submanifold, are studied. For nontrivial realanalytic boundaries we get an extension and uniqueness result, which forces thehypersurface to be real analytic. This allows us to classify all real analyticgeneric boundaries of Levi-flat hypersurfaces in terms of their normalcoordinates. For the remaining case of generic real analytic boundary we get aweaker extension theorem. We find examples to show that these two extensionresults are optimal. Further, a class of nowhere minimal real analyticsubmanifolds is found, which is never the boundary of even a $C^2$ Levi-flathypersurface.Comment: 15 pages; latex, amsrefs; fix statement and proof of theorem 3.1;  accepted in Indiana Univ. Math.

Extension of Levi-flat hypersurfaces past CR boundaries