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تسجيل مستخدم جديدA note on global smoothability of small $L^p$-connection with prescribed curvature
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Siran Li
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We show that if $Omega$ is a connection $1$-form on a vector bundle $eta$ over a closed $n$-dimensional Riemannian manifold $mathcal{M}$ with $L^p$-regularity ($p>n$) and smooth curvature $2$-form $mathscr{F}$, then it can be approximated in the $L^p$-norm by smooth connections of the same curvature, provided that $|Omega|_{L^p(mathcal{M})}$ is smaller than a uniform constant depending only on $p$ and $mathcal{M}$.
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