- 00-359 Rapha\"el CERF
- The Hausdorff lower semicontinuous envelope of
the length in the plane
(377K, Postscript)
Sep 13, 00
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Abstract. 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.
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