Doubling constant mean curvature tori in ${S}^{3}$
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 5 (2006) no. 4, p. 611-638

The Clifford tori in ${S}^{3}$ constitute a one-parameter family of flat, two-dimensional, constant mean curvature (CMC) submanifolds. This paper demonstrates that new, topologically non-trivial CMC surfaces resembling a pair of neighbouring Clifford tori connected at a sub-lattice consisting of at least two points by small catenoidal bridges can be constructed by perturbative PDE methods. That is, one can create a submanifold that has almost everywhere constant mean curvature by gluing a re-scaled catenoid into the neighbourhood of each point of a sub-lattice of the Clifford torus; and then one can show that a constant mean curvature perturbation of this submanifold does exist.

Classification:  53A10,  58J10
@article{ASNSP_2006_5_5_4_611_0,
author = {Butscher, Adrian and Pacard, Frank},
title = {Doubling constant mean curvature tori in $S^3$},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 5},
number = {4},
year = {2006},
pages = {611-638},
zbl = {1170.53303},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2006_5_5_4_611_0}
}

Butscher, Adrian; Pacard, Frank. Doubling constant mean curvature tori in $S^3$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 5 (2006) no. 4, pp. 611-638. http://www.numdam.org/item/ASNSP_2006_5_5_4_611_0/

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