A sub-additive inequality for the volume spectrum

2020/06/22 by Dey, Akashdeep
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.12468

Abstract

Let (M,g) be a closed Riemannian manifold and \ω_p\_p=1^∞ be the volume spectrum of (M,g). We will show that ω_k+m+1≤ ω_k+ω_m+W for all k,m≥ 0, where ω₀=0 and W is the one-parameter Almgren-Pitts width of (M,g). We will also prove the similar inequality for the ε-phase-transition spectrum \c_ε(p)\_p=1^∞ using the Allen-Cahn approach.

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