References of "International Mathematics Research Notices"
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See detailGradient Estimates on Dirichlet and Neumann Eigenfunctions
Arnaudon, Marc; Thalmaier, Anton UL; Wang, Feng-Yu

in International Mathematics Research Notices (in press)

By methods of stochastic analysis on Riemannian manifolds, we derive explicit two-sided gradient estimates for Dirichlet eigenfunctions on a d-dimensional compact Riemannian manifold D with boundary ... [more ▼]

By methods of stochastic analysis on Riemannian manifolds, we derive explicit two-sided gradient estimates for Dirichlet eigenfunctions on a d-dimensional compact Riemannian manifold D with boundary. Corresponding two-sided gradient estimates for Neumann eigenfunctions are derived in the second part of the paper. [less ▲]

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See detailPrescribing metrics on the boundary of AdS 3-manifolds
Tamburelli, Andrea UL

in International Mathematics Research Notices (2016)

We prove that given two metrics g+ and g− with curvature κ<−1 on a closed, oriented surface S of genus τ≥2, there exists an AdS manifold N with smooth, space-like, strictly convex boundary such that the ... [more ▼]

We prove that given two metrics g+ and g− with curvature κ<−1 on a closed, oriented surface S of genus τ≥2, there exists an AdS manifold N with smooth, space-like, strictly convex boundary such that the induced metrics on the two connected components of ∂N are equal to g+ and g−. Using the duality between convex space-like surfaces in AdS3, we obtain an equivalent result about the prescription of the third fundamental form. [less ▲]

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See detailDominating Surface group representations by Fuchsian ones
Deroin, Bertrand; Tholozan, Nicolas UL

in International Mathematics Research Notices (2015)

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See detailWilson Lines from Representations of NQ-Manifolds
Bonechi, Francesco; Zabzine, Maxim; Qiu, Jian UL

in International Mathematics Research Notices (2013), 2013(24),

An NQ-manifold is a nonnegatively graded supermanifold with a degree 1 homological vector field. The focus of this paper is to define the Wilson loops/lines in the context of NQ-manifolds and to study ... [more ▼]

An NQ-manifold is a nonnegatively graded supermanifold with a degree 1 homological vector field. The focus of this paper is to define the Wilson loops/lines in the context of NQ-manifolds and to study their properties. The Wilson loops/lines, which give the holonomy or parallel transport, are familiar objects in usual differential geometry, we analyze the subtleties in the generalization to the NQ-setting and we also sketch some possible applications of our construction. [less ▲]

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See detailThe A_infty de Rham theorem and integration of representations up to homotopy
Arias Abad, Camilo; Schatz, Florian UL

in International Mathematics Research Notices (2013), 2013(16), 3790-3855

We use Chen's iterated integrals to integrate representations up to homotopy. That is, we construct an A-infinity functor from the representations up to homotopy of a Lie algebroid A to those of its ... [more ▼]

We use Chen's iterated integrals to integrate representations up to homotopy. That is, we construct an A-infinity functor from the representations up to homotopy of a Lie algebroid A to those of its infinity groupoid. This construction extends the usual integration of representations in Lie theory. We discuss several examples including Lie algebras and Poisson manifolds. The construction is based on an A-infinity version of de Rham's theorem due to Gugenheim. The integration procedure we explain here amounts to extending the construction of parallel transport for superconnections, introduced by Igusa and Block-Smith, to the case of certain differential graded manifolds. [less ▲]

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See detailStrongly exponential symmetric spaces
Voglaire, Yannick UL

in International Mathematics Research Notices (2013)

We study the exponential map of connected symmetric spaces and characterize, in terms of midpoints and of infinitesimal conditions, when it is a diffeomorphism, generalizing the Dixmier–Saito theorem for ... [more ▼]

We study the exponential map of connected symmetric spaces and characterize, in terms of midpoints and of infinitesimal conditions, when it is a diffeomorphism, generalizing the Dixmier–Saito theorem for solvable Lie groups. We then give a geometric characterization of the (strongly) exponential solvable symmetric spaces as those spaces for which every triangle admits of a unique double triangle. This work is motivated by Weinstein's quantization by groupoids program applied to symmetric spaces. [less ▲]

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See detailDG Affinity of DQ-modules
Petit, François UL

in International Mathematics Research Notices (2012), (6), 1414-1438

In this paper, we prove the dg affinity of formal deformation algebroid stacks over complex smooth algebraic varieties. For that purpose, we introduce the triangulated category of formal deformation ... [more ▼]

In this paper, we prove the dg affinity of formal deformation algebroid stacks over complex smooth algebraic varieties. For that purpose, we introduce the triangulated category of formal deformation modules which are cohomologically complete and whose associated graded module is quasi-coherent. [less ▲]

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See detailTame Galois realizations of $ GSp_4(\Bbb F_łl)$ over $\Bbb Q$
Arias De Reyna Dominguez, Sara UL; Vila, Núria

in International Mathematics Research Notices (2011), (9), 2028--2046

In this paper, we obtain realizations of the 4-dimensional general symplectic group over a prime field of characteristic l> 3 as the Galois group of a tamely ramified Galois extension of Q. The strategy ... [more ▼]

In this paper, we obtain realizations of the 4-dimensional general symplectic group over a prime field of characteristic l> 3 as the Galois group of a tamely ramified Galois extension of Q. The strategy is to consider the Galois representation ρ_l attached to the Tate module at l of a suitable abelian surface. We need to choose the abelian surfaces carefully in order to ensure that the image of ρ_l is large and simultaneously maintain a control on the ramification of the corresponding Galois extension. We obtain an explicit family of curves of genus 2 such that the Galois representation attached to the l-torsion points of their Jacobian varieties provides tame Galois realizations of the desired symplectic groups. [less ▲]

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See detailMulti-black holes and earthquakes on Riemann surfaces with boundaries
Bonsante, Francesco; Krasnov, Kirill; Schlenker, Jean-Marc UL

in International Mathematics Research Notices (2011), (3), 487--552

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