NONCLASSICAL MINIMIZING SURFACES WITH SMOOTH BOUNDARY

Camillo De Lellis; Guido De Philippis; Jonas Hirsch

doi:10.4310/JDG/1669998183

NONCLASSICAL MINIMIZING SURFACES WITH SMOOTH BOUNDARY

Camillo De Lellis, Guido De Philippis, Jonas Hirsch

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We construct a Riemannian metric g on R⁴(arbitrarily close to the euclidean one) and a smooth simple closed curve Γ ⊂ R⁴such that the unique area minimizing surface spanned by Γ has infinite topology. Furthermore the metric is almost Kähler and the area minimizing surface is calibrated.

Original language	English (US)
Pages (from-to)	205-222
Number of pages	18
Journal	Journal of Differential Geometry
Volume	122
Issue number	2
DOIs	https://doi.org/10.4310/JDG/1669998183
State	Published - Oct 2022

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology

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10.4310/JDG/1669998183

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abstract = "We construct a Riemannian metric g on R4(arbitrarily close to the euclidean one) and a smooth simple closed curve Γ ⊂ R4such that the unique area minimizing surface spanned by Γ has infinite topology. Furthermore the metric is almost K{\"a}hler and the area minimizing surface is calibrated.",

author = "{De Lellis}, Camillo and {De Philippis}, Guido and Jonas Hirsch",

note = "Funding Information: and Emmy Murphy for several interesting discussions. The work of G.D.P is supported by the INDAM grant “Geometric Variational Problems”. Publisher Copyright: {\textcopyright} 2022 International Press of Boston, Inc.. All rights reserved.",

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N2 - We construct a Riemannian metric g on R4(arbitrarily close to the euclidean one) and a smooth simple closed curve Γ ⊂ R4such that the unique area minimizing surface spanned by Γ has infinite topology. Furthermore the metric is almost Kähler and the area minimizing surface is calibrated.

AB - We construct a Riemannian metric g on R4(arbitrarily close to the euclidean one) and a smooth simple closed curve Γ ⊂ R4such that the unique area minimizing surface spanned by Γ has infinite topology. Furthermore the metric is almost Kähler and the area minimizing surface is calibrated.

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NONCLASSICAL MINIMIZING SURFACES WITH SMOOTH BOUNDARY

Abstract

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