On some recent developments of the theory of sets of finite perimeter
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 14 (2003) no. 3, pp. 179-187.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In this paper we describe some recent progress on the theory of sets of finite perimeter, currents, and rectifiability in metric spaces. We discuss the relation between intrinsic and extrinsic theories for rectifiability
@article{RLIN_2003_9_14_3_a1,
     author = {Ambrosio, Luigi},
     title = {On some recent developments of the theory of sets of finite perimeter},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {179--187},
     publisher = {mathdoc},
     volume = {Ser. 9, 14},
     number = {3},
     year = {2003},
     zbl = {1225.49039},
     mrnumber = {1823840},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2003_9_14_3_a1/}
}
TY  - JOUR
AU  - Ambrosio, Luigi
TI  - On some recent developments of the theory of sets of finite perimeter
JO  - Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
PY  - 2003
SP  - 179
EP  - 187
VL  - 14
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RLIN_2003_9_14_3_a1/
LA  - en
ID  - RLIN_2003_9_14_3_a1
ER  - 
%0 Journal Article
%A Ambrosio, Luigi
%T On some recent developments of the theory of sets of finite perimeter
%J Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
%D 2003
%P 179-187
%V 14
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RLIN_2003_9_14_3_a1/
%G en
%F RLIN_2003_9_14_3_a1
Ambrosio, Luigi. On some recent developments of the theory of sets of finite perimeter. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 14 (2003) no. 3, pp. 179-187. http://geodesic.mathdoc.fr/item/RLIN_2003_9_14_3_a1/

[1] L. Ambrosio, Some fine properties of sets of finite perimeter in Ahlfors regular metric measure spaces. Adv. Math., 59, 2001, 51-67. | DOI | MR | Zbl

[2] L. Ambrosio, Fine properties of sets of finite perimeter in doubling metric measure spaces. Set Valued Analysis, to appear. | DOI | MR | Zbl

[3] L. Ambrosio - B. Kirchheim, Rectifiable sets in metric and Banach spaces. Math. Ann., 318, 2000, 527-555. | DOI | MR | Zbl

[4] L. Ambrosio - B. Kirchheim, Currents in metric spaces. Acta Math., 185, 2000, 1-80. | DOI | MR | Zbl

[5] A. Baldi, Weighted BV functions. Houston J. of Math., 27(3), 2001, 683-705. | MR | Zbl

[6] I. Birindelli - E. Lanconelli, A negative answer to a one-dimensional symmetry problem in the Heisenberg group. Calc. Var., to appear. | fulltext mini-dml | DOI | MR | Zbl

[7] J. Cheeger, Differentiability of Lipschitz functions on metric measure spaces. Geometric and Functional Analysis, 9, 1999, 428-517. | DOI | MR | Zbl

[8] E. De Giorgi, Nuovi teoremi relativi alle misure $(r-1)$-dimensionali in uno spazio a $r$ dimensioni. Ricerche Mat., 4, 1955, 95-113. | MR | Zbl

[9] E. De Giorgi, Problema di Plateau generale e funzionali geodetici. Atti Sem. Mat. Fis. Univ. Modena, 43, 1995, 285-292. | MR | Zbl

[10] H. Federer - W.H. Fleming, Normal and integral currents. Ann. of Math., 72, 1960, 458-520. | MR | Zbl

[11] H. Federer, A note on the Gauss-Green theorem. Proc. Amer. Math. Soc., 9, 1958, 447-451. | MR | Zbl

[12] B. Franchi - R. Serapioni - F. Serra Cassano, Sets of finite perimeter in the Heisenberg group. C. R. Acad. Sci. Paris, 329, 1999, 183-188. | DOI | MR | Zbl

[13] B. Franchi - R. Serapioni - F. Serra Cassano, Rectifiability and Perimeter in the Heisenberg group. Math. Ann., to appear. | DOI | MR | Zbl

[14] B. Franchi - R. Serapioni - F. Serra Cassano, On the structure of finite perimeter sets in step 2 Carnot groups. Preprint. | DOI | MR | Zbl

[15] N. Garofalo - D.M. Nhieu, Isoperimetric and Sobolev Inequalities for Carnot-Carathéodory Spaces and the Existence of Minimal Surfaces. Comm. Pure Appl. Math., 49, 1996, 1081-1144. | DOI | MR | Zbl

[16] E. Giusti, Minimal surfaces and functions of bounded variation. Birkhäuser, 1984. | MR | Zbl

[17] V. Magnani, Differentiability and area formula on stratified Lie groups. Houston J. of Math., 27(2), 2001, 297-323. | MR | Zbl

[18] M. Miranda Jr., Functions of bounded variation on «good» metric measure spaces. Preprint Scuola Normale Superiore 2000, to appear in J. Math. Pures Appliquées. | Zbl

[19] S.D. Pauls, Minimal surfaces in the Heisenberg group. Forthcoming. | fulltext mini-dml | DOI | MR | Zbl

[20] S.K. Vodop'Yanov, $\mathcal{P}$-differentiability on Carnot groups in different topologies and related topics. Proc. on Analysis and Geometry, Sobolev Institute Press, Novosibirsk 2000, 603-670. | MR | Zbl