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• W2951417464 abstract "We prove that some Riemannian manifolds with boundary under an explicit integral pinching are spherical space forms. Precisely, we show that 3-dimensional Riemannian manifolds with totally geodesic boundary, positive scalar curvature and an explicit integral pinching between the $L^2$-norm of their scalar curvature and the $L^2$-norm of their Ricci tensor are spherical space forms with totally geodesic boundary. Moreover, we prove also that 4-dimensional Riemannian manifolds with umbilic boundary, positive Yamabe invariant and an explicit integral pinching between the total integral of their $(Q,T)$-curvature and the $L^2$-norm of their Weyl curvature are spherical space forms with totally geodesic boundary. As a consequence of our work, we show that a certain conformally invariant operator which plays an important role in Conformal Geometry has a trivial kernel and is non-negative if the Yamabe invariant is positive and verifies a pinching condition together with the total integral of the $(Q,T)$-curvature. As an application of the latter spectral analysis, we show the existence of conformal metrics with constant $Q$-curvature, constant $T$-curvature, and zero mean curvature under the latter assumptions." @default.
• W2951417464 created "2019-06-27" @default.
• W2951417464 creator A5050140290 @default.
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• W2951417464 date "2008-11-24" @default.
• W2951417464 modified "2023-10-01" @default.
• W2951417464 title "Integral pinching results for manifolds with boundary" @default.
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• W2951417464 hasPublicationYear "2008" @default.
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