1,721,024 research outputs found
Symmetry for Solutions of Two-phase Semilinear Elliptic Equations on Hyperbolic Space
No full textAssume that f ( s ) = F ′ ( s ) where F is a double-well potential. Under certain conditions on the Lipschitz constant of f on [ − 1 , 1 ] , we prove that arbitrary bounded global solutions of the semilinear equation Δ u = f ( u ) on hyperbolic space H n must reduce to functions of one variable provided they admit asymptotic boundary values on S n − 1 = ∂ ∞ H n which are invariant under a cohomogeneity one subgroup of the group of isometries of H n . We also prove existence of these one-dimensional solutions
The index of Dirac operators on manifolds with fibered boundaries
Full text linkLet X be a compact manifold with boundary ∂X, and suppose that ∂X is the total space of a fibration Z → ∂X → Y. Let D Φ be a generalized Dirac operator associated to a Φ-metric gΦ on X. Under the assumption that DΦ is fully elliptic we prove an index formula for DΦ. The proof is in two steps: first, using results of Melrose and Rochon, we show that the index is unchanged if we pass to a certain b-metric gb(ε). Next we write the b- (i.e. the APS) index formula for gb(ε); the Φ-index formula follows by analyzing the limiting behaviour as ε ↘ 0 of the two terms in the formula. The interior term is studied directly whereas the adiabatic limit formula for the eta invariant follows from work of Bismut and Cheeger
On the asymptotic geometry of the Hitchin metric
No full textI will report on recent joint work with Rafe Mazzeo, Jan Swoboda and Frederik Witt on the asymptotic geometry of the Hitchin metric. This is the natural metric on the moduli space of Higgs bundles. We describe the difference to a more elementary semiflat metric, thus confirming part of a more general proposal of Gaiotto, Moore and Neitzke.Non UBCUnreviewedAuthor affiliation: University of KielFacult
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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