The Isoperimetric Inequality in Steady Ricci Solitons

Abstract

The author proves that the isoperimetric inequality on the graphic curves over circle or hyperplanes over ${\mathbb{S}^{n - 1}}$ is satisfied in the cigar steady soliton and in the Bryant steady soliton. Since both of them are Riemannian manifolds with warped product metric, the author utilize the result of Guan-Li-Wang to get his conclusion. For the sake of the soliton structure, the author believes that the geometric restrictions for manifolds in which the isoperimetric inequality holds are naturally satisfied for steady Ricci solitons.

Keywords

Isoperimetric inequality / Ricci soliton

References

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