| 1. |
- Andersson, Lars, et al.
(författare)
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scalar curvature rigidity for asymptotically locally hyperbolic manifolds
- 1998
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Ingår i: Annals of Global Analysis and Geometry. - 0232-704X .- 1572-9060. ; 16, s. 1-27
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Tidskriftsartikel (refereegranskat)abstract
- Rigidity results for asymptotically locally hyperbolic manifoldswith lower bounds on scalar curvature are proved using spinor methodsrelated to the Witten proof of the positive mass theorem. The argument isbased on a study of the Dirac operator defined with respect to the Killingconnection. The existence of asymptotic Killing spinors is related to thespin structure on the end. The expression for the mass is calculated andproven to vanish for conformally compact Einstein manifolds with conformalboundary a spherical space form, giving rigidity. In the 4-dimensional case,the signature of the manifold is related to the spin structure on the end andexplicit formulas for the relevant invariants are given.
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| 2. |
- Constantin, Adrian, et al.
(författare)
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On geodesic exponential maps of the Virasoro group
- 2007
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Ingår i: Annals of Global Analysis and Geometry. - : Springer Science and Business Media LLC. - 1572-9060 .- 0232-704X. ; 31:2, s. 155-180
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Tidskriftsartikel (refereegranskat)abstract
- We study the geodesic exponential maps corresponding to Sobolev type right-invariant (weak) Riemannian metrics mu((k)) (k >= 0) on the Virasoro group Vir and show that for k >= 2, but not for k = 0, 1, each of them defines a smooth Frechet chart of the unital element e is an element of Vir. In particular, the geodesic exponential map corresponding to the Korteweg - de Vries (KdV) equation ( k = 0) is not a local diffeomorphism near the origin.
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| 3. |
- Dahl, Mattias
(författare)
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Dirac eigenvalues for generic metrics on three-manifolds
- 2003
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Ingår i: Annals of Global Analysis and Geometry. - 0232-704X .- 1572-9060. ; 24, s. 95-100
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Tidskriftsartikel (refereegranskat)abstract
- We show that for generic Riemannian metrics on a closed spin manifold of dimension three the Dirac operator has only simple eigenvalues.
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| 4. |
- Fedosova, Ksenia, et al.
(författare)
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Second variation of Selberg zeta functions and curvature asymptotics
- 2020
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Ingår i: Annals of Global Analysis and Geometry. - : Springer Science and Business Media LLC. - 1572-9060 .- 0232-704X. ; 57:1, s. 23-60
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Tidskriftsartikel (refereegranskat)abstract
- We give an explicit formula for the second variation of the logarithm of the Selberg zeta function, Z(s), on Teichmüller space. We then use this formula to determine the asymptotic behavior as Rs→ ∞ of the second variation. As a consequence, for m∈ N, we obtain the complete expansion in m of the curvature of the vector bundle H(Xt, Kt) → t∈ T of holomorphic m-differentials over the Teichmüller space T, for m large. Moreover, we show that this curvature agrees with the Quillen curvature up to a term of exponential decay, O(m2e-l0m), where l is the length of the shortest closed hyperbolic geodesic.
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| 5. |
- Gudmundsson, Sigmundur, et al.
(författare)
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Harmonic morphisms from homogeneous Hadamard manifolds
- 2011
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Ingår i: Annals of Global Analysis and Geometry. - : Springer Science and Business Media LLC. - 1572-9060 .- 0232-704X. ; 39, s. 215-230
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Tidskriftsartikel (refereegranskat)abstract
- We present a new method for manufacturing complex-valued harmonic morphisms from a wide class of Riemannian Lie groups. This yields new solutions from an important family of homogeneous Hadamard manifolds. We also give a new method for constructing left-invariant foliations on a large class of Lie groups producing harmonic morphisms.
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| 6. |
- Gudmundsson, Sigmundur, et al.
(författare)
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Harmonic morphisms from the Grassmannians and their non-compact duals
- 2006
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Ingår i: Annals of Global Analysis and Geometry. - : Springer Science and Business Media LLC. - 1572-9060 .- 0232-704X. ; 30:4, s. 313-333
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we give a unified framework for the construction of complex valued harmonic morphisms from the real, complex and quaternionic Grassmannians and their non-compact duals. This gives a positive answer to the corresponding open existence problem in the real and quaternionic cases.
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| 7. |
- Gudmundsson, Sigmundur, et al.
(författare)
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Proper r-harmonic functions from Riemannian manifolds
- 2020
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Ingår i: Annals of Global Analysis and Geometry. - : Springer Science and Business Media LLC. - 0232-704X .- 1572-9060. ; 57, s. 217-223
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a new method for constructing complex-valued r-harmonic functions on Riemannian manifolds. We then apply this for the important semisimple Lie groups SO(n) , SU(n) , Sp(n) , SLn(R) , Sp(n, R) , SU(p, q) , SO(p, q) , Sp(p, q) , SO∗(2 n) and SU∗(2 n).
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| 8. |
- Gudmundsson, Sigmundur, et al.
(författare)
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r-Harmonic and complex isoparametric functions on the Lie groups Rm⋉Rn and Rm⋉H2n+1
- 2020
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Ingår i: Annals of Global Analysis and Geometry. - : Springer Science and Business Media LLC. - 1572-9060 .- 0232-704X. ; 58:4, s. 477-496
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we introduce the notion of complex isoparametric functions on Riemannian manifolds. These are then employed to devise a general method for constructing proper r-harmonic functions. We then apply this to construct the first known explicit proper r-harmonic functions on the Lie group semidirect products Rm⋉ Rn and Rm⋉ H 2n+1, where H 2n+1 denotes the classical (2 n+ 1) -dimensional Heisenberg group. In particular, we construct such examples on all the simply connected irreducible four-dimensional Lie groups.
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| 9. |
- Kolsrud, Torbjörn, et al.
(författare)
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Foliated manifolds and conformal heat morphisms
- 2002
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Ingår i: Annals of Global Analysis and Geometry. - 0232-704X .- 1572-9060. ; 21:3, s. 241-267
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Tidskriftsartikel (refereegranskat)abstract
- The objects under study, in this article, are Riemannian manifolds foliated by hypersurfaces. Looking at the transverse direction as time, we construct the generalised heat operator and, in the spirit of a time-space extension of harmonic morphisms, we introduce the conformal heat morphisms. Concrete examples of these concepts are presented, as well as, a characterisation of conformal heat morphisms. Lastly, we calculate the heat Lie algebra of the generalised heat operator.
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| 10. |
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