The isoperimetric problem in the Grushin space h+1 with density |x| p
Rendiconti del Seminario Matematico della Università di Padova, Tome 139 (2018), pp. 241-260.

In this paper we study the isoperimetric problem in a class of x-spherically symmetric sets in the Grushin space h+1 with density |x| p , p>-h+1. 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 ( x , y ) h + 1 : | y | < arcsin | x | π 2 sin α + 1 ( t ) d t , | x | < 1 .

DOI : 10.4171/RSMUP/139-10
Classification : 53, 49
Mots-clés : Grushin space, density, weighted isoperimetric problem
He, Guoqing 1 ; Zhao, Peibiao 2

1 Anhui Normal University, Wuhu City, China and Nanjing University of Science and Technology, Nanjing, China
2 Nanjing University of Science and Technology, Nanjing, China
@article{RSMUP_2018__139__241_0,
     author = {He, Guoqing and Zhao, Peibiao},
     title = {The isoperimetric problem in the {Grushin} space $\mathbb{R}^{h+1}$ with density $|x|^p$},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {241--260},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {139},
     year = {2018},
     doi = {10.4171/RSMUP/139-10},
     mrnumber = {3825189},
     zbl = {1406.53037},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/139-10/}
}
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He, Guoqing; Zhao, Peibiao. The isoperimetric problem in the Grushin space $\mathbb{R}^{h+1}$ with density $|x|^p$. Rendiconti del Seminario Matematico della Università di Padova, Tome 139 (2018), pp. 241-260. doi : 10.4171/RSMUP/139-10. http://www.numdam.org/articles/10.4171/RSMUP/139-10/

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