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Characteristic points, rectifiability and perimeter measure on stratified groups

Valentino Magnani (2006)

Journal of the European Mathematical Society

We establish an explicit connection between the perimeter measure of an open set E with C 1 boundary and the spherical Hausdorff measure S Q 1 restricted to E , when the ambient space is a stratified group endowed with a left invariant sub-Riemannian metric and Q denotes the Hausdorff dimension of the group. Our formula implies that the perimeter measure of E is less than or equal to S Q 1 ( E ) up to a dimensional factor. The validity of this estimate positively answers a conjecture raised by Danielli, Garofalo...

Characterization of cycle domains via Kobayashi hyperbolicity

Gregor Fels, Alan Huckleberry (2005)

Bulletin de la Société Mathématique de France

A real form G of a complex semi-simple Lie group G has only finitely many orbits in any given G -flag manifold Z = G / Q . The complex geometry of these orbits is of interest, e.g., for the associated representation theory. The open orbits D generally possess only the constant holomorphic functions, and the relevant associated geometric objects are certain positive-dimensional compact complex submanifolds of D which, with very few well-understood exceptions, are parameterized by the Wolf cycle domains Ω W ( D ) in...

Characterization of E -subcompactification

Abdolmajid Fattahi, H. R. Ebrahimi Vishki (2006)

Archivum Mathematicum

For extending the notion of E -algebra, as defined in [2], we present an example of an m-admissible algebra which is not an E - algebra. Then we define E -subcompactification and E -subcompactification to study the universal E -subcompactification and the universal E -subcompactification from the function algebras point of view.

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