The tangency of a C^1 smooth submanifold with respect to a non-involutive C^1 distribution has no superdensity points

DOI10.1512/IUMJ.2019.68.7549zbMath1427.58001OpenAlexW2943480832MaRDI QIDQ5225160

Silvano Delladio

Publication date: 19 July 2019

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1512/iumj.2019.68.7549

zbMATH Keywords

Frobenius theoremtangency set of a submanifold with respect to a distributionsuperdensity

Mathematics Subject Classification ID

Pfaffian systems (58A17) Integration on manifolds; measures on manifolds (58C35) Vector distributions (subbundles of the tangent bundles) (58A30)

Related Items (11)

A closure result for differential forms in the context of superdensity, approximation of measurable functions by density-degree functions ⋮ A Lusin type result ⋮ Approximate continuity and differentiability with respect to density degree, an application to BV and Sobolev functions ⋮ Superdensity with respect to a Radon measure on \(\mathbb{R}^n\) ⋮ Structure results for the integral set of a submanifold with respect to a non-integrable exterior differential system ⋮ Involutivity of distributions at points of superdense tangency with respect to normal currents ⋮ Weak stationarity of a matrix valued differential form at superdensity points of its vanishing set ⋮ \(m\)-approximate Taylor polynomial ⋮ Good behaviour of Lie bracket at a superdensity point of the tangency set of a submanifold with respect to a rank 2 distribution ⋮ A fine property of sets at points of Lebesgue density ⋮ On the geometric structure of currents tangent to smooth distributions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Functions of class \(C^1\) subject to a Legendre condition in an enhanced density set
• Characteristic points, rectifiability and perimeter measure on stratified groups
• A Lusin type theorem for gradients
• On the structure of finite perimeter sets in step 2 Carnot groups
• Structure of tangencies to distributions via the implicit function theorem
• Size of characteristic sets and functions with prescribed gradient
• Size of tangencies to non-involutve distributions
• Sur un théorème de traces. (On a trace theorem)

This page was built for publication: The tangency of a C^1 smooth submanifold with respect to a non-involutive C^1 distribution has no superdensity points