Isoperimetric sets on Carnot groups

By Gian Paolo Leonardi, Séverine Rigot. 2003

93 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/df56d717fd30fdfae5ff5a26243d7c8b878838bc

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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): “very recently with a continuously growing literature and it is now the subject of several contributions: [1], [5], [8], [12], [15], [17], [26]–[30], [32], [41], [45]–[48], [54], [57], [60]–[62], [67], and this list is certainly not complete.”
Regularity of C1 smooth surfaces with prescribed p-mean curvature in the Heisenberg group (2007, unknown): “D G ] 2 4 Ju l 2”
Regularity of Sets with Quasiminimal Boundary Surfaces in Metric Spaces (2011, background): “ns of this paper to successfully address rectiﬁability issues in this weighted Euclidean setting. For related results about isoperimetric sets in the Carnot group settingwe refertheinterested readerto[LR], where they show thatisoperimetric sets (which are necessarily a special class of sets of quasi”
Geometry of Carnot-Caratheodory Spaces, Differentiability, Coarea and Area Formulas (2009, unknown): “Rigot [94], W.”
Convex isoperimetric sets in the Heisenberg group (2006, background): “Isoperimetric sets do exist: this is proved in [12] by a concentration-compactness argument.”
A Notable Family of Entire Intrinsic Minimal Graphs in the Heisenberg Group which are not Perimeter Minimizing (2006, unknown): “e over the past decade, see [Pa1], [Pa2], [CDG], [KR], [E1], [E2], [E3], [Gro], [GN], [Be], [DS], [DGN1], [AK1], [AK2], [CS1], [A], [FSS1], [Ma1], [FSS2], [Ma2], [CMS], [FSS3], [BRS], [DGN4], [DGN5], [LR], [LM], [FSS4], [Ma3], [CS2] [P1], [P2], [GP], [CG], [CHMY], [CH], [HP1], [HP2], [RR], [BC], [Se”
TOWARDS DIFFERENTIAL CALCULUS IN STRATIFIED GROUPS (2007, background): “e we mention a list of references for a rough overview that is certainly far from being complete, [1], [3], [4], [7], [8], [9], [11], [12], [13], [14], [15], [20], [21], [22], [24], [28], [33], [35], [36], [42], [44], [43], [46], [47], [48], [52], [56]. In the present work the notion of diﬀerentiabi”