On a Correlation Inequality for Cauchy Type Measures

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New Zealand Journal of Mathematics

Vol. 45, (2015), Pages 53-64


Yashar Memarian

University of Notre-Dame,

Indiana,

United States.

mailto:y.memarian@gmail.com






Abstract In this paper we present a correlation inequality with respect to Cauchy type measures. To prove our inequality, we transport the problem onto the Riemannian sphere then state and solve some special cases for a spherical correlation problem. This method, as we shall explain, opens up a new class of interesting problems related to correlation type inequalities.

Keywords Cauchy Measures, Correlation problems,Spherical Brunn- Theorem, Spherical Correlation Problem, Waist of positively Curved Riemannian Manifolds.

Classification (MSC2000) 52A20, 60D05.

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