Some remarks on the variation of curve length and surface area
نویسندگان
چکیده
منابع مشابه
Some Remarks on the Variation of Curve Length and Surface Area
Consider the curve C = {(t, f(t): 0 < t < 1}, where f is absolutely continuous on [0, 1]. Then C has finite length, and if Ue is the &neighborhood of f in the uniform norm, we compare the length of the shortest path in UE with the length of f. Our main result establishes necessary and sufficient conditions on f such that the difference of these quantities is of order e as e -* 0. We also includ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1996
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-96-03087-0