Four-manifolds with positive yamabe constant
WebOct 1, 2015 · We prove that a positive definite smooth four-manifold with $b_2^+ \geq 2$ and having either no 1-handles or no 3-handles cannot admit a symplectic structure. WebMay 1, 2024 · As applications, we give some rigidity theorems on four-manifolds with positive Yamabe constant. We recover generalize the conformally invarisome of …
Four-manifolds with positive yamabe constant
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WebIn his study of Ricci flow, Perelman introduced a smooth-manifold invariant called ¯λ. We show here that, for completely elementary reasons, this invariant simply equals the … WebThe conformal Yamabe constant is usually defined only for compact manifolds; here we also allow non-compact manifolds in the definition. This will turn out to be essential for …
WebIn his study of Ricci flow, Perelman introduced a smooth-manifold invariant called ¯λ. We show here that, for completely elementary reasons, this invariant simply equals the Yamabe invariant, alias the sigma constant, whenever the latter is non-positive. On the other hand, the Perelman invariant just equals +∞ whenever the Yamabe Web: Let M be a compact four-dimensional manifold with non-positive Yamabe invariant. Then Y (M) = Y (M #(S1 × S3)). Using the results of LeBrun mentioned previously we get new exact computations of the invariant: Proposition 4 : Let X be a minimal compact complex surface of general type.
WebAs applications, we give some rigidity theorems on four-manifolds with postive Yamabe constant. In particular, these rigidity theorems are sharp for our conditions have the … WebAug 1, 2024 · In our setting, we first apply the Yamabe constant to get the Yamabe-Sobolev inequality and furthermore get a logarithmic Sobolev inequality on closed …
WebApr 6, 2024 · Request PDF Ricci Flow under Kato-type curvature lower bound In this work, we extend the existence theory of non-collapsed Ricci flows from point-wise curvature lower bound to Kato-type lower ...
WebOct 6, 2014 · The Yamabe invariant of simply connected manifolds. J. Petean. Mathematics. 1998. We prove that the Yamabe invariant of any simply connected smooth manifold of dimension n greater than four is non-negative. Equivalently that the infimum of the L^ {n/2} norm of the scalar curvature,…. 53. bas barWebGiven a CR manifold(M2n+1,J),we can define the subbundle T1,0of the complexified tangent bundle as the+i-eigenspace of J,and T0,1as its conjugate.We likewise denote byΛ1,0the space of(1,0)-forms(that is,the subbundle ofwhich annihilates T0,1)and byΛ0,1its conjugate.The CR structure is said to be integrable if T0,1is closed under the Lie ... sv italia u14WebFour- and Six-Manifolds of Positive Scalar Curvature and Positive Euler Characteristic Matthew J. Gursky Abstract. In this paper, we prove that a compact 4- or 6 dimensional … svitalhttp://math.umd.edu/~jmr/Yamabe.pdf bas barkarby bibliotekWebAug 23, 2024 · The Weyl functional on 4-manifolds of positive Yamabe invariant Chanyoung Sung Annals of Global Analysis and Geometry 60 , 767–805 ( 2024) Cite this article 165 Accesses Metrics Abstract It is shown that on every closed oriented Riemannian 4-manifold ( M , g) with positive scalar curvature, sv italia u13WebNov 1, 2012 · Recently, Kim [11] has studied the rigidity phenomena for Bach-flat manifolds and derived that a complete noncompact Bach-flat four-manifold (M 4, g) with nonnegative constant scalar curvature and the positive Yamabe constant is an Einstein manifold if the L 2-norm of R ∘ m is small enough. bas barbellWebFor a four manifold with a positive Yamabe constant, it follows from the solution of the Yamabe problem ([Au], [S]) that we may assume that g is the Yamabe metric which attains the Yamabe constant, then Rg is a constant and (1.7) Z M ˙2(Ag)dvg Z M 1 24 R2 gdvg = 1 24 (R M Rgdvg)2 vol(g) 1 24 (R M Rcdvg c)2 (vol(gc)) = 16ˇ2; bas bartels