Some Fine Properties of Sets of Finite Perimeter in Ahlfors Regular Metric Measure Spaces

By Luigi Ambrosio. 2001

172 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7dbbf6235014f062eaeff1e120a67a58f7e0c626

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Fine Properties of Sets of Finite Perimeter in Doubling Metric Measure Spaces (2002, background): “Fine properties of sets of finite perimeter in doubling metric measure spaces Luigi Ambrosio Scuola Normale Superiore Piazza Cavalieri 7 56100 Pisa, Italy e-mail: luigi@ambrosio.sns.it May 2002”
A Notable Family of Entire Intrinsic Minimal Graphs in the Heisenberg Group which are not Perimeter Minimizing (2006, methodology): “Lemma 3.8. On a surface S as in Lemma 3.7, one has − Z! = A ,”
The BV-capacity in metric spaces (2010, background): “The theory of BV-functions in metric measure spaces, see [24, 1, 2], with results like coarea formula and lower semicontinuity of the variation measure play an essential role in our approach.”
Functions of bounded variation on “good” metric spaces (2003, background): “, 1999; emmes, nifold functions I am deeply grateful to L. Ambrosio for his helpful suggestions and his support. particularly indebted with S. Semmes and J. Heinonen for the useful discussions with I thank V. Magnani and E. Paolini for their advices and suggestions.”
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.”
On gradient bounds for the heat kernel on the Heisenberg group (2007, background): “so [35]). From (27), we get similarly for any ball B in Hand any Borel set A ⊂ Bc with smooth boundary, µt,x(A) ≤ CB,t,xµ surface t,x (∂A). (29) 6.3 Bobkov type isoperimetric inequalities Let Fγ : R→ [0,1] be the cumulative probability function of the standard Gaussian distribution γ on the real lin”
The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations (2006, methodology): “Moreover, introducing a suitable intrinsic notions of rectifiability in a Carnot group of step 2, a counterpart of De Giorgi’s result on the structure of sets of finite Euclidean perimeter (see, for instance, [30]) has been obtained in [24] (see also [ 3 ], [41],[34],[35],).”
Surface measures in Carnot-Carathéodory spaces (2001, background): “More recently, introducing a suitable intrinsic notion of rectifiability in the Heisenberg group, a counterpart of De Giorgi’s result on the structure of sets of finite Euclidean perimeter (see [32]) has been obtained in [29] (see Sect. 5 and see also [ 2 ] and [52]).”