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The geometry of stable minimal surfaces in metric Lie groups by Meeks, William H.; Mira, Pablo; Perez, Joaquin is a scholarly article available to read on EtoBox.

What is The geometry of stable minimal surfaces in metric Lie groups about?

We study geometric properties of compact stable minimal surfaces with boundary in homogeneous 3-manifolds $X$ that can be expressed as a semidirect product of $\mathbb{R}^2$ with $\mathbb{R}$ endowed with a left invariant metric. For any such compact minimal surface $M$, we provide a priori radius estimate which depends only on the maximum distance of points of the boundary $\partial M$ to a vertical geodesic of $X$. We also give a generalization of the classical Rado's Theorem in $\mathbb{R}^3$ to the context of compact minimal surfaces with graphical boundary over a convex horizontal domain in $X$, and we study the geometry, existence and uniqueness of this type of Plateau problem.

Author

Meeks, William H.; Mira, Pablo; Perez, Joaquin

Published

2016

Language

EN