Communications in Analysis and Geometry

Volume 23 (2015)

Number 4

A uniqueness theorem for gluing calibrated submanifolds

Pages: 691 – 715

DOI: http://dx.doi.org/10.4310/CAG.2015.v23.n4.a1

Author

Yohsuke Imagi (Kavli Institute for the Physics and Mathematics of the Universe (IPMU), Kashiwa, Japan)

Abstract

‘Gluing’ is a technique of constructing solutions to non-linear (elliptic) partial differential equations such as Yang–Mills equations, minimal surface equations and Einstein equations. Calibrated submanifolds are a certain class of minimal surfaces, and there are various examples of them constructed by the gluing technique. We have existence theorems in that sense, but there seems to have been no uniqueness theory for higher-dimensional ones such as special Lagrangian submanifolds, which we discuss in the present paper.

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Published 13 August 2015