Abstract
On a closed balanced manifold, we show that if the Chern scalar curvature is small enough in a certain Sobolev norm, then a slightly modified version of the Chern–Yamabe flow (Angella et al. in On Chern–Yamabe Problem, 2015) converges to a solution of the Chern–Yamabe problem. We also prove that if the Chern scalar curvature, on closed almost-Hermitian manifolds, is close enough to a constant function in a Hölder norm, then the Chern–Yamabe problem has a solution for generic values of the fundamental constant.
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The first named author is supported in part by a PSC-CUNY Award \(\#\) 60053-00 48, jointly funded by The Professional Staff Congress and The City University of New York.
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Lejmi, M., Maalaoui, A. On the Chern–Yamabe Flow. J Geom Anal 28, 2692–2706 (2018). https://doi.org/10.1007/s12220-017-9929-6
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DOI: https://doi.org/10.1007/s12220-017-9929-6