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Selfdual gauge field vortices: an analytical approach
No full textIn modern theoretical physics, gauge field theories are of great importance since they keep internal symmetries and account for phenomena such as spontaneous symmetry breaking, the quantum Hall effect, charge fractionalization, superconductivity and supergravity. This monograph discusses specific examples of gauge field theories that exhibit a selfdual structure.The author builds a foundation for gauge theory and selfdual vortices by introducing the basic mathematical language of the subject and formulating examples ranging from the well-known abelian–Higgs and Yang–Mills models to the Chern–Simons–Higgs theories (in both the abelian and non-abelian settings). Thereafter, the electroweak theory and self-gravitating electroweak strings are also examined, followed by the study of the differential problems that have emerged from the analysis of selfdual vortex configurations; in this regard the author treats elliptic problems involving exponential non-linearities, also in relation to concentration-compactness principles and blow-up analysis.
Many open questions still remain in the field and are examined in this comprehensive work in connection with Liouville-type equations and systems. The goal of this text is to form an understanding of selfdual solutions arising in a variety of physical contexts. Selfdual Gauge Field Vortices: An Analytical Approach is ideal for graduate students and researchers interested in partial differential equations and mathematical physics
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
Minimal immersions of closed surfaces in hyperbolic 3-manifold.
No full textMotivated by the the work of K. Uhlenbeck, we discuss minimal
immersions of closed surfaces of genus larger than 1 on hyperbolic
3-manifold. In this respect we establish multiple existence for the
Gauss-Codazzi equations and describe the asymptotic behaviour of the
solutions in terms of the prescribed conformal structure and holomorphic
quadratic differential whose real part identifies the corresponding
second fundamental form.
Joint work with Z. Huang and M. LuciaNon UBCUnreviewedAuthor affiliation: Roma Tor VergataFacult
Asymptotics for minimizers of a Donaldson functional and mean curvature 1-immersions of surfaces into hyperbolic 3-manifolds
No full textIt has been shown in by Huang-Lucia-Tarantello [17] that, for given , the moduli space of constant mean curvature (CMC) -immersions of
a closed orientable surface of genus into a hyperbolic
-manifold can be parametrized by elements of the tangent bundle of the
corresponding Teichm\"uller space. This is attained by showing the unique
solvability of the Gauss-Codazzi equations governing (CMC) c-immersions. The
corresponding unique solution is identified as the global minimum (and only
critical point) of the Donaldson functional (introduced in [11]) given in
(1.3) with .
When (i.e. ), so far nothing is known about
the existence of analogous (CMC) c-immersions. Indeed, for the
functional may no longer be bounded from below and evident
non-existence situations do occur.
Already the case (i.e. ) appears rather involved and
actually (CMC) 1-immersions can be attained only as "limits" of (CMC)
c-immersions for . To handle this
situation, here we analyse the asymptotic behaviour of minimizers of as
.
We use an accurate asymptotic analysis to describe possible blow-up
phenomena. In this way, we can relate the existence of (CMC) 1-immersions to
the Kodaira map. As a consequence, we obtain the first existence and uniqueness
result about (CMC) 1-immersions of surfaces of genus into
hyperbolic 3-manifolds
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