WebPositive scalar curvature and exotic aspherical manifolds - Jialong DENG 邓嘉龙, YMSC Scalar curvature is interesting not only in analysis, geometry and topology but also in physics. For example, the positive mass theorem, which was proved by Schoen and Yau in 1979, is equivalent to the result that the three-dimension torus carries no Riemannian … Web1 time t′ ∈ [−1, 0] has length 2ǫ−1 and scalar curvature (1 − t′ )−1 . A metric on S2 × I, such that each point is contained in some ǫ-neck, is called an ǫ-tube, or an ǫ-horn, or a double ǫ-horn, if the scalar curvature stays bounded on both ends, stays bounded on one end and tends to infinity on the other, and tends to ...
An integral inequality for constant scalar curvature metrics on K ...
Web19 aug. 2015 · A well-known question in differential geometry is to control the constant in isoperimetric inequality by intrinsic curvature conditions. In dimension 2, the constant can be controlled by the integral of the positive part of the Gaussian curvature. WebIn differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold.It can be considered, broadly, as a measure of the degree to which the geometry of a given metric tensor differs locally from that of ordinary Euclidean space or … how to add jabra earbuds to pc
A Quantitative Analysis of Metrics on - Oxford Academic
WebThis inequality agrees with the obvious one in the 2-sphere (where the conventionally defined scalar curvature equals twice the sectional curvature) where the widths of the … Web1 okt. 2024 · In this paper, we study the interplay of geometry and positive scalar curvature on a complete, non-compact manifold with non-negative Ricci curvature. On three-dimensional manifold, ... , Metric inequalities with scalar curvature, Geom. Funct. Anal. 28 (2024), no. 3, 645–726. 10.1007/s00039-018-0453-z Search in Google Scholar WebGromov M., Metric inequalities with scalar curvature, Geom. Funct. Anal.28(2024), 645-726, arXiv:1710.04655. Gromov M., Four lectures on scalar curvature, arXiv:1908.10612. Gromov M., Lawson Jr. H.B., Spin and scalar curvature in the presence of a fundamental group. I, Ann. of Math.111(1980), 209-230. method laundry detergent workout clothes