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Sharp Estimate of Global Coulomb Gauge
Communications on Pure and Applied Mathematics ( IF 2.676 ) Pub Date : 2020-09-13 , DOI: 10.1002/cpa.21939
Yu Wang

Let A be a W1, 2‐connection on a principal SU(2)‐bundle P over a compact 4‐manifold M whose curvature FA satisfies urn:x-wiley:00103640:media:cpa21939:cpa21939-math-0001. Our main result is the existence of a global section σ : M → P with finite singularities on M such that the connection form σ*A satisfies the Coulomb equation d*(σ*A) = 0 and admits a sharp estimate urn:x-wiley:00103640:media:cpa21939:cpa21939-math-0002. Here 4, ∞ is a new function space we introduce in this paper that satisfies L4(M) ⊊ ℒ4, ∞(M) ⊊ L4 − ϵ(M) for all ϵ > 0. More precisely, 4, ∞(M) is the collection of measurable function u such that urn:x-wiley:00103640:media:cpa21939:cpa21939-math-0003, where L4, ∞ is the classical Lorentz space and su is the L4‐integrability radius function associated to u defined by urn:x-wiley:00103640:media:cpa21939:cpa21939-math-0004 Briefly speaking, we achieve the estimate of urn:x-wiley:00103640:media:cpa21939:cpa21939-math-0005 by showing that σ*A is effectively L4‐integrable away from controllably many points on M. © 2020 Wiley Periodicals LLC
更新日期:2020-10-17

 

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