Abstract
We prove that conformal metrics on domains of the round sphere, with non-negative constant Q-curvature, and non-negative scalar curvature, has positive mean curvature on the boundary of embedded balls (in the round metric). As a result, such metrics have certain reflection symmetries if the complement of the domain is contained in a lower-dimensional round sphere. We also prove that the development map of a locally conformally flat metric with non-positive Schouten tensor is an embedding.
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Chang, SY.A., Han, ZC., Yang, P. (2020). Some Remarks on the Geometry of a Class of Locally Conformally Flat Metrics. In: Chen, J., Lu, P., Lu, Z., Zhang, Z. (eds) Geometric Analysis. Progress in Mathematics, vol 333. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-34953-0_3
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DOI: https://doi.org/10.1007/978-3-030-34953-0_3
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-34952-3
Online ISBN: 978-3-030-34953-0
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