# Generalizing the Linearized Doubling Approach and New Minimal Surfaces and Self-Shrinkers via Doubling

13 Jan 2020 Kapouleas Nikolaos McGrath Peter

In Part I of this article we generalize the Linearized Doubling (LD) approach which has been introduced by NK, to apply (under reasonable assumptions) to doubling arbitrary closed minimal surfaces in arbitrary Riemannian three-manifolds without any symmetry requirements. More precisely assume given a family of LD solutions on a closed minimal surface $\Sigma$ embedded in a Riemannian three-manifold, where an LD solution $\varphi$ is a solution with logarithmic singularities of the linearized equation $(\Delta+|A|^2+\Ric(\nu,\nu)\,)\varphi =0$ on $\Sigma$... (read more)

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