Global gauges and global extensions in optimal spaces
| Autor: | Mircea Petrache, Tristan Rivière |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics nonlinear extension MathematicsofComputing_GENERAL Yang–Mills existence and mass gap conformally invariant problem Space (mathematics) 58J05 Mathematics - Geometric Topology Critical space Hopf lift FOS: Mathematics 46E35 58D15 58E15 49Q20 46E30 43A80 47J07 46T30 58C15 55R10 57M50 46E35 70S15 nonlinear Sobolev space Mathematics Numerical Analysis Applied Mathematics 28A51 Geometric Topology (math.GT) Extension (predicate logic) Yang–Mills Functional Analysis (math.FA) Sobolev space Mathematics - Functional Analysis Differential Geometry (math.DG) Lorentz spaces global gauge Analysis |
| Zdroj: | Anal. PDE 7, no. 8 (2014), 1851-1899 |
| ISSN: | 1851-1899 |
| Popis: | We consider the problem of extending functions \phi:\to S^n to functions u:B^{n+1}\to S^n for n=2,3. We assume \phi to belong to the critical space W^{1,n} and we construct a W^{1,(n+1,\infty)}-controlled extension u. The Lorentz-Sobolev space W^{1,(n+1,\infty)} is optimal for such controlled extension. Then we use such results to construct global controlled gauges for L^4-connections over trivial SU(2)-bundles in 4 dimensions. This result is a global version of the local Sobolev control of connections obtained by K. Uhlenbeck. Comment: 60 pages |
| Databáze: | OpenAIRE |
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