The isoperimetric problem in the Grushin space with density

  • Guoqing He

    Anhui Normal University, Wuhu City, China and Nanjing University of Science and Technology, Nanjing, China
  • Peibiao Zhao

    Nanjing University of Science and Technology, Nanjing, China

Abstract

In this paper we study the isoperimetric problem in a class of -spherically symmetric sets in the Grushin space with density , . First we prove the existence of weighted isoperimetric sets. Then we deduce that, up to a vertical translation, a dilation and a negligible set, the weighted isoperimetric set is only of the form .

Cite this article

Guoqing He, Peibiao Zhao, The isoperimetric problem in the Grushin space with density . Rend. Sem. Mat. Univ. Padova 139 (2018), pp. 241–260

DOI 10.4171/RSMUP/139-10