Mathematical Theory and Applications ›› 2021, Vol. 41 ›› Issue (3): 13-37.

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Mean Field Equation on Spheres

  

  1. 1.Department of Mathematics, The University of Texas at San Antonio, TX 78249, USA; 2. School of Mathematics and Statistics, Central South University, Changsha 410075, China.
  • Online:2021-09-30 Published:2021-10-28
  • Contact: Gui Changfeng；E−mail：changfeng.gui@utsa.edu

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Abstract: In this expository note, we will introduce the recent progress and open problems concerning mean field type equations on spheres. In particular, some new inequalities of Aubin-Onofri type as well as their close connection to mean field type equations are presented. 

Key words: Mean field equation;Paneitz operator, Conformal metric, Szego limit theorem, Moser-Trudinger inequality

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