Let $H\colon\mathbb{R}^{3}\to\mathbb{R}$ be a $C^{1}$ mapping such that $H(p)\to \H_{\infty}>0$ as $|p|\to\infty$. We show that when $H$ satisfies some global conditions then there exists an $H$-bubble, namely a sphere $S$ in $\mathbb{R}^{3}$ such that the mean curvature of $S$ at any regular point $p\in S$ equals $H(p)$.
Bubbles with prescribed mean curvature: The variational approach
CALDIROLI, Paolo;
2011-01-01
Abstract
Let $H\colon\mathbb{R}^{3}\to\mathbb{R}$ be a $C^{1}$ mapping such that $H(p)\to \H_{\infty}>0$ as $|p|\to\infty$. We show that when $H$ satisfies some global conditions then there exists an $H$-bubble, namely a sphere $S$ in $\mathbb{R}^{3}$ such that the mean curvature of $S$ at any regular point $p\in S$ equals $H(p)$.
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