{"title":"From valuations on convex bodies to convex functions","authors":"Jonas Knoerr, Jacopo Ulivelli","doi":"10.1007/s00208-024-02902-z","DOIUrl":null,"url":null,"abstract":"<p>A geometric framework relating valuations on convex bodies to valuations on convex functions is introduced. It is shown that a classical result by McMullen can be used to obtain a characterization of continuous, epi-translation invariant, and <i>n</i>-epi-homogeneous valuations on convex functions, which was previously established by Colesanti, Ludwig, and Mussnig. Following an approach by Goodey and Weil, a new characterization of 1-epi-homogeneous valuations is obtained.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"43 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Annalen","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00208-024-02902-z","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
A geometric framework relating valuations on convex bodies to valuations on convex functions is introduced. It is shown that a classical result by McMullen can be used to obtain a characterization of continuous, epi-translation invariant, and n-epi-homogeneous valuations on convex functions, which was previously established by Colesanti, Ludwig, and Mussnig. Following an approach by Goodey and Weil, a new characterization of 1-epi-homogeneous valuations is obtained.
期刊介绍：
Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin.
The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin.
Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.
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