Regular domains in homogeneous groups

By Roberto Monti, Daniele Morbidelli. 2005

50 citations recorded by the source corpus.

We study John, uniform and non-tangentially accessible domains in homogeneous groups of steps 2 and 3. We show that C 1,1 domains in groups of step 2 are non-tangentially accessible and we give an explicit condition which ensures the John property in groups of step 3.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/79327144f5e06bc65981757e141dc246cdab94d3

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In Applied Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry on Carnot groups (2009, background): “It continues our program in this area [5, 4, 7], which is one component in a worldwide endeavor investigating sub-Riemannian geometric measure theory, including theories of rectifiability and perimeter [14], [26], [27], [17], [42], [3], [39]; fractals and tilings [56], [57]; geometric analysis of no”
Characteristic points, rectifiability and perimeter measure on stratified groups (2006, background): “Characteristic points play an important role in connection with metric properties of domains suitable for Sobolev–Poincaré inequality, Ahlfors regularity of hypersurfaces, intrinsic measure of hypersurfaces and trace theorems [8], [12], [15], [16], [22], [31], [48], [55], [56].”