Two counterexamples in low-dimensional length geometry
نویسندگان
چکیده
منابع مشابه
Two Counterexamples in Low-dimensional Length Geometry
One of the key properties of the length of a curve is its lower semicontinuity : if a sequence of curves γi converges to a curve γ, then length(γ) ≤ lim inf length(γi). Here the weakest type of pointwise convergence suffices. There are higher-dimensional analogs of this semicontinuity for Riemannian (and even Finsler) metrics. For instance, the Besicovitch inequality (see, e.g., [1] and [4]) im...
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ژورنال
عنوان ژورنال: St. Petersburg Mathematical Journal
سال: 2007
ISSN: 1061-0022
DOI: 10.1090/s1061-0022-07-00984-3