کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4667879 | 1633858 | 2007 | 21 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Valuations with Crofton formula and Finsler geometry
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
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چکیده انگلیسی
Valuations admitting a smooth Crofton formula are studied using Geometric Measure Theory and Rumin's cohomology of contact manifolds. The main technical result is a current representation of a valuation with a smooth Crofton formula. A geometric interpretation of Alesker's product is given for such valuations. As a first application in Finsler geometry, a short proof of the theorem of Gelfand–Smirnov that Crofton densities are projective is derived. The Holmes–Thompson volumes in a projective Finsler space are studied. It is shown that they induce in a natural way valuations and that the Alesker product of the k-dimensional and the l-dimensional Holmes–Thompson valuation is the (k+l)-dimensional Holmes–Thompson valuation.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 210, Issue 2, 1 April 2007, Pages 733-753
Journal: Advances in Mathematics - Volume 210, Issue 2, 1 April 2007, Pages 733-753