| 1. |
- Ammann, Bernd, et al.
(författare)
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Smooth yamabe invariant and surgery
- 2013
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Ingår i: Journal of differential geometry. - : International Press of Boston. - 0022-040X .- 1945-743X. ; 94:1, s. 1-58
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Tidskriftsartikel (refereegranskat)abstract
- We prove a surgery formula for the smooth Yamabe invariant sigma(M) of a compact manifold M. Assume that N is obtained from M by surgery of codimension at least 3. We prove the existence of a positive constant Lambda(n), depending only on the dimension n of M, such that sigma(N) >= min{sigma(M), Lambda(n)}.
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| 2. |
- Andersson, Lars, et al.
(författare)
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A new tensorial conservation law for Maxwell fields on the Kerr background
- 2017
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Ingår i: Journal of Differential Geometry. - : International Press of Boston. - 0022-040X .- 1945-743X. ; 105:2, s. 163-176
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Tidskriftsartikel (refereegranskat)abstract
- A new, conserved, symmetric tensor field for a source-free Maxwell test field on a four-dimensional spacetime with a conformal Killing-Yano tensor, satisfying a certain compatibility condition, is introduced. In particular, this construction works for the Kerr spacetime.
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| 3. |
- Arnlind, Joakim, et al.
(författare)
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Multi-linear Formulation of Differential Geometry and Matris Regularizations
- 2012
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Ingår i: Journal of differential geometry. - : International Press. - 0022-040X .- 1945-743X. ; 91:1, s. 1-39
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Tidskriftsartikel (refereegranskat)abstract
- We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi-linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for Weingartens formula, the Ricci curvature, and the Codazzi-Mainardi equations. For matrix analogues of embedded surfaces, we define discrete curvatures and Euler characteristics, and a non-commutative Gauss-Bonnet theorem is shown to follow. We derive simple expressions for the discrete Gauss curvature in terms of matrices representing the embedding coordinates, and explicit examples are provided. Furthermore, we illustrate the fact that techniques from differential geometry can carry over to matrix analogues by proving that a bound on the discrete Gauss curvature implies a bound on the eigenvalues of the discrete Laplace operator.
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| 4. |
- Berman, Robert, 1976
(författare)
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CONICAL CALABI-YAU METRICS ON TORIC AFFINE VARIETIES AND CONVEX CONES
- 2023
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Ingår i: Journal of Differential Geometry. - 1945-743X .- 0022-040X. ; 125:2, s. 345-377
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that any affine toric variety Y , which is Q-Gorenstein, admits a conical Ricci flat Kähler metric, which is smooth on the regular locus of Y . The corresponding Reeb vector is the unique minimizer of the volume functional on the Reeb cone of Y . The case when the vertex point of Y is an isolated singularity was previously shown by Futaki–Ono–Wang. The proof is based on an existence result for the inhomogeneous Monge–Ampère equation in Rm with exponential right hand side and with prescribed target given by a proper convex cone, combined with transversal a priori estimates on Y .
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| 5. |
- Berndtsson, Bo, 1950
(författare)
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Positivity of direct image bundles and convexity on the space of Kähler metrics.
- 2009
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Ingår i: Journal of differential geometry. - : International Press of Boston. - 0022-040X .- 1945-743X. ; 81:3, s. 457-482
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Tidskriftsartikel (refereegranskat)abstract
- We develop some results from [4] on the positivity of direct image bundles in the particular case of a trivial fibration over a one-dimensional base. We also apply the results to study variations of Kähler metrics.
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| 6. |
- Bischoff, Francis, et al.
(författare)
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Morita equivalence and the generalized Kähler potential
- 2022
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Ingår i: Journal of differential geometry. - : International Press of Boston. - 0022-040X .- 1945-743X. ; 121:2, s. 187-226
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Tidskriftsartikel (refereegranskat)abstract
- We solve the problem of determining the fundamental degrees of freedom underlying a generalized Kahler structure of symplectic type. For a usual Kahler structure, it is well-known that the geometry is determined by a complex structure, a Kahler class, and the choice of a positive (1, 1)-form in this class, which depends locally on only a single real-valued function: the Kahler potential. Such a description for generalized Kahler geometry has been sought since it was discovered in 1984. We show that a generalized Kahler structure of symplectic type is determined by a pair of holomorphic Poisson manifolds, a holomorphic symplectic Morita equivalence between them, and the choice of a positive Lagrangian brane bisection, which depends locally on only a single real-valued function, which we call the generalized Kahler potential. Our solution draws upon, and specializes to, the many results in the physics literature which solve the problem under the assumption (which we do not make) that the Poisson structures involved have constant rank. To solve the problem we make use of, and generalize, two main tools: the first is the notion of symplectic Morita equivalence, developed by Weinstein and Xu to study Poisson manifolds; the second is Donaldson's interpretation of a Kahler metric as a real Lagrangian submanifold in a deformation of the holomorphic cotangent bundle.
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| 7. |
- Chantraine, Baptiste, et al.
(författare)
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Floer theory for Lagrangian cobordisms
- 2020
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Ingår i: Journal of differential geometry. - : INT PRESS BOSTON, INC. - 0022-040X .- 1945-743X. ; 114:3, s. 393-465
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Tidskriftsartikel (refereegranskat)abstract
- In this article we define intersection Floer homology for exact Lagrangian cobordisms between Legendrian submanifolds in the contactisation of a Liouville manifold, provided that the Chekanov-Eliashberg algebras of the negative ends of the cobordisms admit augmentations. From this theory we derive several long exact sequences relating the Morse homology of an exact Lagrangian cobordism with the bilinearised contact homologies of its ends. These are then used to investigate the topological properties of exact Lagrangian cobordisms.
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| 8. |
- Cianchi, Andrea, et al.
(författare)
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On the discreteness of the spectrum of the Laplacian on noncompact Riemannian manifolds
- 2011
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Ingår i: Journal of differential geometry. - : International Press. - 0022-040X .- 1945-743X. ; 87:3, s. 469-491
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Tidskriftsartikel (refereegranskat)abstract
- Necessary and sufficient conditions for the discreteness of the Laplacian on a noncompact Riemannian manifold M are established in terms of the isocapacitary function of M. The relevant capacity takes a different form according to whether M has finite or infinite volume. Conditions involving the more standard isoperimetric function of M can also be derived, but they are only sufficient in general, as we demonstrate by concrete examples.
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| 9. |
- Dimitroglou Rizell, Georgios, 1982-, et al.
(författare)
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Refined disk potentials for immersed lagrangian surfaces
- 2022
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Ingår i: Journal of differential geometry. - : INTERNATIONAL PRESS BOSTON, INC. - 0022-040X .- 1945-743X. ; 121:3, s. 459-539
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Tidskriftsartikel (refereegranskat)abstract
- We define a refined Gromov-Witten disk potential of monotone immersed Lagrangian surfaces in a symplectic 4-manifold that are self-transverse as an element in a capped version of the Chekanov- Eliashb erg dg-algebra of the singularity links of the double points (a collection of Legendrian Hopf links). We give a surgery formula that expresses the potential after smoothing a double point. We study refined potentials of monotone immersed Lagrangian spheres in the complex projective plane and find monotone spheres that cannot be displaced from complex lines and conics by symplectomorphisms. We also derive general restrictions on sphere potentials using Legendrian lifts to the contact 5-sphere.
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| 10. |
- Ekholm, Tobias, 1970-, et al.
(författare)
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Legendrian contact homology in the boundary of a subcritical Weinstein 4-manifold
- 2015
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Ingår i: Journal of differential geometry. - Boston. - 0022-040X .- 1945-743X. ; 101:1, s. 67-157
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Tidskriftsartikel (refereegranskat)abstract
- We give a combinatorial description of the Legendrian contact homology algebra associated to a Legendrian link in S1×S2 or any connected sum #k(S1×S2), viewed as the contact boundary of the Weinstein manifold obtained by attaching 1-handles to the 4-ball. In view of the surgery formula for symplectic homology, this gives a combinatorial description of the symplectic homology of any 4-dimensional Weinstein manifold (and of the linearized contact homology of its boundary). We also study examples and discuss the invariance of the Legendrian homology algebra under deformations, from both the combinatorial and the analytical perspectives
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