Ulam floating functions
Chunyan Liu, Elisabeth M. Werner, Deping Ye, and Ning Zhang
TL;DR
This paper introduces Ulam floating functions, extending the concept from convex bodies to functions, and derives a new variational formula for the affine surface area of log-concave functions.
Contribution
It generalizes Ulam floating sets to functions and provides a novel variational formula for affine surface area of log-concave functions.
Findings
Derived a new variational formula for affine surface area
Extended Ulam floating sets to functions
Provides theoretical foundation for further research
Abstract
We extend the notion of Ulam floating sets from convex bodies to Ulam floating functions. We use the Ulam floating functions to derive a new variational formula for the affine surface area of log-concave functions.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topology and Set Theory · Analytic and geometric function theory · Point processes and geometric inequalities