“Almgren regularity theorem”的意思、由来-开放百科全书

词条

Almgren regularity theorem

释义

References

In geometric measure theory, a field of mathematics, the Almgren regularity theorem, proved by {{harvs |txt |last=Almgren |authorlink=Frederick J. Almgren, Jr. |year1=1983 |year2=2000}}, states that the singular set of a mass-minimizing surface has codimension at least 2. Almgren's proof of this was 955 pages long.

References

{{Citation | last1=Almgren | first1=F. J. | title=Q valued functions minimizing Dirichlet's integral and the regularity of area minimizing rectifiable currents up to codimension two | doi=10.1090/S0273-0979-1983-15106-6 | mr=684900 | year=1983 | journal=American Mathematical Society. Bulletin. New Series | issn=0002-9904 | volume=8 | issue=2 | pages=327–328}}
{{Citation

| last1=Almgren | first1=Frederick J. Jr.
| editor1-last=Taylor | editor1-first=Jean E. | editor1-link= Jean Taylor
| editor2-last=Scheffer | editor2-first=Vladimir | editor2-link= Vladimir Scheffer
| title=Almgren's big regularity paper. Q-valued functions minimizing Dirichlet's integral and the regularity of area-minimizing rectifiable currents up to codimension 2
| url=https://books.google.com/books?isbn=9810241089
| publisher= World Scientific
| location=River Edge, NJ
| series=World Scientific Monograph Series in Mathematics
| isbn=978-981-02-4108-7
| year=2000
| volume=1
| mr=1777737
| zbl= 0985.49001
}}

{{Citation | last1=Chang | first1=Sheldon X. | title=On Almgren's regularity result | doi=10.1007/BF02922666 | mr=1731058 | year=1998 | journal=The Journal of Geometric Analysis | issn=1050-6926 | volume=8 | issue=5 | pages=703–708}}
{{Citation | last1=White | first1=Brian | authorlink = Brian White (mathematician) | title=The mathematics of F. J. Almgren, Jr | doi=10.1007/BF02922665 | mr=1731057 | year=1998 | journal=The Journal of Geometric Analysis | issn=1050-6926 | volume=8 | issue=5 | pages=681–702| citeseerx=10.1.1.120.4639 }}

2 : Theorems in measure theory|Theorems in geometry

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