On the rectifiability of domains with finite perimeter
L. A. Caffarelli, N. M. Rivière (1976)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Displaying similar documents to “Euclidean quasiconvexity.”
On the rectifiability of domains with finite perimeter
Extension of internally bilipschitz maps in John disks.
Broch, Ole Jacob (2006)
Annales Academiae Scientiarum Fennicae. Mathematica
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On the imbedding of subsets of a metric space in Jordan continua
R. Wilder (1932)
Fundamenta Mathematicae
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The Hausdorff lower semicontinuous envelope of the length in the plane
Raphaël Cerf (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We study the Hausdorff lower semicontinuous envelope of the length in the plane. This envelope is taken with respect to the Hausdorff metric on the space of the continua. The resulting quantity appeared naturally as the rate function of a large deviation principle in a statistical mechanics context and seems to deserve further analysis. We provide basic simple results which parallel those available for the perimeter of Caccioppoli and De Giorgi.
On the shortest curve which meets all the lines which meet a circle
Vance Faber, Jan Mycielski, Paul Pedersen (1984)
Annales Polonici Mathematici
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Boundaries in digital planes.
Khalimsky, Efim, Kopperman, Ralph, Meyer, Paul R. (1990)
Journal of Applied Mathematics and Stochastic Analysis
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J. E. McMillan's Area theorem
Michael O'Neill (1999)
Colloquium Mathematicae
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A simply connected, homogeneous domain that is not a quasidisk.
Hjelle, Geir Arne (2005)
Annales Academiae Scientiarum Fennicae. Mathematica
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One-to-one continuous images of a line
F. Jones (1970)
Fundamenta Mathematicae
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Generalized John disks
Chang-Yu Guo, Pekka Koskela (2014)
Open Mathematics
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We establish the basic properties of the class of generalized simply connected John domains.
Concerning the common boundary of two domains
R. Moore (1924)
Fundamenta Mathematicae
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The main purpose of the present paper is to show that if a bounded continuum has more then one prime part and no one of its prime parts separates the plane then in order that it should have just two complementary domains and be the complete boundary of each of them it is necessary and sufficient that it should remain connected in the weak sense on the removal of any one of its connected proper subsets which is closed.