
arXiv: 1909.08274
We derive an integral inequality between the mean curvature and the scalar curvature of the boundary of any scalar flat conformal compactifications of Poincaré-Einstein manifolds. As a first consequence, we obtain a sharp lower bound for the first eigenvalue of the conformal half-Laplacian of the boundary of such manifolds. Secondly, a new upper bound for the renormalized volume is given in the four dimensional setting. Finally, some estimates on the first eigenvalues of Dirac operators are also deduced.
Mathematics - Differential Geometry, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Spectral problems; spectral geometry; scattering theory on manifolds, FOS: Mathematics, Rigidity results, Spin and Spin\({}^c\) geometry, Conformal structures on manifolds, 530, Applications of global differential geometry to the sciences, 510
Mathematics - Differential Geometry, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Spectral problems; spectral geometry; scattering theory on manifolds, FOS: Mathematics, Rigidity results, Spin and Spin\({}^c\) geometry, Conformal structures on manifolds, 530, Applications of global differential geometry to the sciences, 510
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 0 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
