Global gauges and global extensions in optimal spaces
Petrache, Mircea · Rivière, Tristan
Original · EN
We consider the problem of extending functions ϕ:→ Sⁿ to functions u:Bⁿ⁺¹→ Sⁿ for n=2,3. We assume ϕto belong to the critical space W¹,ⁿ and we construct a W¹,⁽ⁿ⁺¹,∞⁾-controlled extension u. The Lorentz-Sobolev space W¹,⁽ⁿ⁺¹,∞⁾ is optimal for such controlled extension. Then we use such results to construct global controlled gauges for L⁴-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.
English translation
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