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On Bonnesen-Style Symmetric Mixed Isohomothetic Inequality In ℝ2

Authors
  • Wang, Yuanyuan1
  • Wang, Xingxing2
  • Zeng, Chunna3
  • 1 Wuhan University of Science and Technology, College of Science, Wuhan, 430081, China , Wuhan (China)
  • 2 Shanghai Lixin University of Accounting and Finance, School of Mathematics and Statistics, Shanghai, 201620, China , Shanghai (China)
  • 3 Chongqing Normal University, School of Mathematical Sciences, Chongqing, 401331, China , Chongqing (China)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer Singapore
Publication Date
Jul 10, 2019
Volume
39
Issue
5
Pages
1319–1329
Identifiers
DOI: 10.1007/s10473-019-0510-1
Source
Springer Nature
Keywords
License
Yellow

Abstract

In this paper, we investigate the translative containment measure for a convex domain Ki to contain, or to be contained in the homothetic copy of another convex domain tKj (t ≥ 0). Via the formulas of translative Blaschke and Poincaré in integral formula, we obtain a Bonnesen-style symmetric mixed isohomothetic inequality. The Bonnesen-style symmetric mixed isohomothetic inequality obtained is known as Bonnesen-style inequality if one of the domains is a disc. As a direct consequence, we attain an inequality which strengthen the result proved by Bonnesen, Blaschké and Flanders. Furthermore, by the containment measure and Blaschke’s rolling theorem, we obtain the reverse Bonnesen-style symmetric mixed isohomothetic inequalities. These inequalities are the analogues of the known Bottema’s result in 1933.

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