Work

𝐿_{𝑝}-Blaschke valuations

Year: 2015

Type: article

Abstract: In this article, a classification of continuous, linearly intertwining, symmetric L p L_p -Blaschke ( p > 1 p>1 ) valuations is established as an extension of Haberl’s work on Blaschke valuations. More precisely, we show that for dimensions n ≥ 3 n \geq 3 , the only continuous, linearly intertwining, normalized symmetric L p L_p -Blaschke valuation is the normalized L p L_p -curvature image operator, while for dimension n = 2 n = 2 , a rotated normalized L p L_p -curvature image operator is the only additional one. One of the advantages of our approach is that we deal with normalized symmetric L p L_p -Blaschke valuations, which makes it possible to handle the case p = n p=n . The cases where p ≠ n p \not =n are also discussed by studying the relations between symmetric L p L_p -Blaschke valuations and normalized ones.

Source: Transactions of the American Mathematical Society

DOI: 10.1090/s0002-9947-2015-06047-4

Authors: Jin Li, Shufeng Yuan, Gangsong Leng

Institution: Shanghai University

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: National Natural Science Foundation of China, Shanghai Leading Academic Discipline Project

Awards: G4596872531, G559074124, G6358221353