Stable minimal surfaces in flat tori

1986 ◽  
pp. 73-78 ◽  
Author(s):  
Mario J. Micallef
Keyword(s):  
Minimal Surfaces ◽  
Flat Tori

scholarly journals Transverse J-holomorphic curves in nearly Kähler $$\mathbb {CP}^3$$

2021 ◽  
Author(s):  
Benjamin Aslan
Keyword(s):  
Minimal Surfaces ◽  
Type Theorem ◽  
Holomorphic Curves ◽  
Nearly Kähler ◽  
Flat Tori

AbstractJ-holomorphic curves in nearly Kähler $$\mathbb {CP}^3$$ CP 3 are related to minimal surfaces in $$S^4$$ S 4 as well as associative submanifolds in $$\Lambda ^2_-(S^4)$$ Λ - 2 ( S 4 ) . We introduce the class of transverse J-holomorphic curves and establish a Bonnet-type theorem for them. We classify flat tori in $$S^4$$ S 4 and construct moment-type maps from $$\mathbb {CP}^3$$ CP 3 to relate them to the theory of $$\mathrm {U}(1)$$ U ( 1 ) -invariant minimal surfaces on $$S^4$$ S 4 .

scholarly journals Trigonal minimal surfaces in flat tori

2007 ◽  
Vol 232 (2) ◽  
pp. 401-422
Author(s):  
Toshihiro Shoda
Keyword(s):  
Minimal Surfaces ◽  
Flat Tori

Minimal surfaces in flat tori

2000 ◽  
Vol 10 (4) ◽  
pp. 679-701 ◽  
Author(s):  
C. Arezzo ◽  
M.J. Micallef
Keyword(s):  
Minimal Surfaces ◽  
Flat Tori

scholarly journals On different notions of calibrations for minimal partitions and minimal networks in ℝ2

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Marcello Carioni ◽  
Alessandra Pluda
Keyword(s):  
Minimal Surfaces ◽  
Steiner Problem ◽  
Minimal Networks

Abstract Calibrations are a possible tool to validate the minimality of a certain candidate. They have been introduced in the context of minimal surfaces and adapted to the case of the Steiner problem in several variants. Our goal is to compare the different notions of calibrations for the Steiner problem and for planar minimal partitions that are already present in the literature. The paper is then complemented with remarks on the convexification of the problem, on nonexistence of calibrations and on calibrations in families.

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