Editors: G. Auchmuty (Houston), H. Brezis (Paris), S. S. Chern
(Berkeley), J. Damon (Chapel Hill), K. Davidson (Waterloo), L. C. Evans
(Berkeley), R. M. Hardt (Rice), J. A. Johnson (Houston), A. Lelek (Houston), J.
Nagata (Osaka), B. H. Neumann (Canberra), G. Pisier (College Station and Paris),
R. Scott (Houston), S. W. Semmes (Rice)
Managing Editor: K. Kaiser (Houston)
Charalambos Charitos, Department of Mathematics, Agricultural University
of Athens, 75 Iera Odos, Athens 11855 Greece, and Georgios Tsapogas,
Department of Mathematics, University of the Agean, Karlovassi, Samos 83200
Greece.
Closed Geodesics on 2-Dimensional chi-Geometric Polyedra pp.185-196.
ABSTRACT.
For 2-dimensional finite chi -geometric polyhedra of curvature K <= chi < 0 it
is shown that the polygonal flow, applied to a closed curve, converges to a
geodesic. Moreover, it is shown that there exists a finite number of closed
geodesics with length smaller than a given positive B. As an application of the
polygonal flow, a way of constructing closed, in particular simple, curves is
given as well as a condition which implies that a curve is non-homotopic to a
point.
Markov, Y., University of North Carolina, Chapel Hill NC
27599-3250
(markov@math.unc.edu),
Tarasov, V., Osaka University, Toyonaka, Osaka 560, Japan
(vt@math.sci.osaka-u.ac.jp),
Varchenko, A., University of North Carolina, Chapel Hill NC
27599-3250
(av@math.unc.edu)
Determinant of a Hypergeometric Period Matrix pp. 197-220.
ABSTRACT. We consider a function
U=e-f0.f1a1
...fpap on a real affine space, here f0,..,fp
are linear functions, a1,...,ap complex numbers. The zeros
of the functions f1,..., fp form an arrangement of
hyperplanes in the affine space. We study the period matrix of the
hypergeometric integrals associated with the arrangement and the function U
and compute its determinant as an alternating product of gamma functions and
critical points of the functions f0,..., fp with respect
to the arrangement.
We also give a determinant formula for Selberg type exponential integrals. In
this case the arangements of hyperplanes is special and admits a symmetry group,
the period matrix is decomposed into blocks corresponding to different
representations of the symmetry group on the space of the hypergeometric
integrals associated with the arrangement. We compute the determinant of the
block corresponding to the trivial representation.
Groisser, David,
University of Florida, Gainesville, FL 32611 (groisser@math.ufl.edu).
Totally geodesic boundaries of Yang-Mills moduli spaces, pp.
221-276.
ABSTRACT. Moduli spaces M of self-dual SU(2)
connections (``instantons'') over a compact Riemannian 4-manifold (M,g) carry a
natural L2 metric g, which is generally incomplete. For
instantons of Pontryagin index 1 over a compact, simply connected, oriented,
positive-definite base manifold, the completion
M is Donaldson's compactification; in fact the boundary of the
completion is an isometric copy of (M,4(pi)2 g) (Groisser and Parker,
1989). In this paper we show that the boundary is, furthermore, a totally
geodesic submanifold of the completion. Along the way, we prove a
regularity theorem: the continuous extension of g to the ``collar
region'' of
M is C 1,alpha (in the conventional scale/center
coordinates) for small, positive alpha. The proofs rely on some new weighted
Sobolev inequalities for concentrated instantons, in which the only dependence
of the Sobolev constants on the connection is through the concentration
parameter lambda. The exponent in the weighting function translates into the
Holder exponent in the regularity theorem.
A. Bonome, R. Castro, E. García-Río, L. Hervella, R. Vázquez-Lorenzo
Departamento de Xeometría e Topoloxía, Facultade de Matemáticas, Universidade de
Santiago de Santiago de Compostela, 15706 Santiago deCompostela , Spain.
On the Paraholomorphic Sectional Curvature of Almost Para-Hermitian
Manifolds, pp. 277-300.
ABSTRACT.
The paraholomorphic sectional curvature of almost para-Hermitian manifolds is
investigated. After discussing those manifolds with pointwise constant
paraholomorphic sectional curvature, main attention is devoted to those being
isotropic. Also, some boundedness conditions for the paraholomorphic sectional
curvature are studied.
Tim Laberge Department of Mathematical Sciences, Northern
Illinois University, DeKalb, IL 60115.
Supports of Quasi-Measures, pp. 301-312.
ABSTRACT.
We define a useful notion of support for quasi-measures on compact Hausdorff
spaces, investigate the consequences of this definition, and prove a
decomposition theorem for quasi-measures. A consequence of the decomposition
theorem is that any space carrying a fully supported 0--1 quasi-measure is
connected and cannot be disconnected by the removal of a closed 0-dimensional
subset.
Fulman, Igor,
University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen O, Denmark
(ifulman@math.ku.dk).
Coordinatization for Fell Bundle Algebras,
pp. 313-324.
ABSTRACT.
Let Cr*(E) be the reduced C*-algebra generated by a Fell bundle E
over an r-discrete principal groupoid. We show that each element in Cr*(E)
is represented by a continuous section of E.
Also, the Coordinatization Theorem proved in this paper gives necessary and
sufficient conditions for an abstract C*-algebra A to be isomorphic to Cr*(E)
for some Fell bundle E.
Fernando Cobos, Depto. de Análisis Matemático, Facultad de Matemáticas,
Universidad Complutense de Madrid, 28040 Madrid, Spain and Tomas Schonbeck,
Florida Atlantic University, Dept. of Mathematical Sciences, Boca Raton, Fl
33431, USA.
On a Theorem by Lions and Peetre About Interpolation Between a Banach Space
and its Dual, pp. 325-344.
ABSTRACT.
We show that if the duality between a Banach space A and its anti-dual A* is
given by the inner product of a Hilbert space H, then (A,A*)1/2,2 = H
= (A,A*)[1/2], provided A satisfies certain mild conditions. We do
not assume A is reflexive. Applications are given to normed ideals of operators.
P. Celada, Dipartimento di Scienze Matematiche, UniversitàDegli
Studi Trieste, P. Le Europa 1, I-34127 Trieste, Italia, and A. Cellina
Scuola Internazionale Superiore di Studi Avanzati (SIISSA), Bia Beirut 4,
I-34013 Trieste, Italia.
Existence and Non Existence of Solutions to a Variational Problem on a
Square, pp. 345-375.
ABSTRACT.
A non convex minimum problem on a square arising in shape optimization is
studied. Conditions are discussed for the existence or the non existence of
solutions.
E.M.E. Zayed Department of Mathematics, Faculty of Science,
Zagazig University, Zagazig, Egypt.
Short-Time Asymptotics of the Heat Kernel of the laplacian of a Bounded
Domain with Robin Boundary Conditions, pp. 377-385.
ABSTRACT.
The basic problem in this paper is that of determining some geometrical
properties of a general bounded domain in two or three dimensions with a smooth
boundary where smooth functions are entering the boundary conditions which are
not strictly positive, from complete knowledge of the eigenvalues for the
negative Laplacian, using the asymptotic expansions of the trace of the heat
kernel for short-time t. Further results are obtained.