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
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Valuations with Crofton formula and Finsler geometry
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