Another proof of the existence of homothetic solitons of the inverse mean curvature flow

2020/01/18 by Hsu, Shu-Yu
#35J75 Secondary 53C44 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Primary 35K67

paper · doi:10.48550/arxiv.2001.06596

Abstract

We will give a new proof of the existence of non-compact homothetic solitons of the inverse mean curvature flow (cf. \citeDLW) in ℝⁿ× ℝ, n≥ 2, of the form (r,y(r)) or (r(y),y) where r=|x|, x∈ℝⁿ, is the radially symmetric coordinate and y∈ ℝ. More precisely for any (1)/(n)0, in (μ,∞) which satisfies r(μ)=0 and r_y(μ)=lim_y\searrowμr_y(y)=+∞. We also prove that there exist constants y₂>y₁>0 such that r_y(y)>0 for any μy₁, r_yy(y)<0 for any μ0 for any y>y₂. Moreover lim_{y→ +∞}r(y)=0 and lim_{y→ +∞}yr_y(y)=0.

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