Maximum principles at infinity

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Abstract

We prove a general maximum principle at infinity for properly immersed minimal surfaces with boundary in ℝ3. An important corollary of this maximum principle at infinity is the existence of a fixed sized regular neighborhood for any properly embedded minimal surface of bounded curvature.

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Meeks, W. H., & Rosenberg, H. (2008). Maximum principles at infinity. Journal of Differential Geometry, 79(1), 141–165. https://doi.org/10.4310/jdg/1207834660

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