The purpose of this paper is to introduce the new concept of weighted floating functions associated with log concave or s-concave functions. This leads to new notions of weighted functional affine surface areas. Their relation to more traditional versions of functional affine surface areas as well as to the classical affine surface areas for convex bodies is discussed in detail.
Schütt, C., Thäle, C., Turchi, N., Werner, E. (2025). Weighted floating functions and weighted functional affine surface areas. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 378(12), 8593-8623 [10.1090/tran/9439].
Weighted floating functions and weighted functional affine surface areas
Turchi, N;
2025
Abstract
The purpose of this paper is to introduce the new concept of weighted floating functions associated with log concave or s-concave functions. This leads to new notions of weighted functional affine surface areas. Their relation to more traditional versions of functional affine surface areas as well as to the classical affine surface areas for convex bodies is discussed in detail.
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