NDLI: A variational characterization of complex submanifolds

Content Provider	Springer Nature Link
Author	Arezzo, Claudio Sun, Jun
Copyright Year	2015
Abstract	In this note, we generalize our results in Arezzo and Sun (Reine Angew Math, doi: 10.1515/crelle-2013-0097 , 2012) to integer p-currents of any degree. We prove that if the mass of a current, as a functional of the ambient metric, has a critical or stable point in some special directions, then the current is complex. This holds for any dimension and codimension. We also study a natural functional on the space of currents representing a fixed homology class, closely related to the first derivative of the Mass in our new approach, detecting the deviation of a surface from being holomorphic.
Starting Page	249
Ending Page	277
Page Count	29
File Format	PDF
ISSN	00255831
Journal	Mathematische Annalen
Volume Number	366
Issue Number	1-2
e-ISSN	14321807
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2015-11-03
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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A variational characterization of complex submanifolds