- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 11:55:26
10
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=CMH&vol=74&iss=1&update_since=2024-03-28
Commentarii Mathematici Helvetici
Comment. Math. Helv.
CMH
0010-2571
1420-8946
General
10.4171/CMH
http://www.ems-ph.org/doi/10.4171/CMH
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Swiss Mathematical Society
74
1999
1
Geodesic foliations in Lorentz 3-manifolds
A.
Zeghib
École Normale Supérieure de Lyon, LYON CEDEX 07, FRANCE
Geodesic, lightlike, normal foliation
We study geodesic foliations on manifolds endowed with Lorentz metrics. The (local) theory works formally exactly as in the Riemannian case, if the induced metric on the leaves is non-degenerate. We consider here some local and global properties in the degenerate case
Manifolds and cell complexes
General
1
21
10.1007/s000140050073
http://www.ems-ph.org/doi/10.1007/s000140050073
Surfaces à points doubles isolés
J.
d'Almeida
Université Lille I, VILLENEUVE D'ASCQ CEDEX, FRANCE
Branch curve, nodes, cusps, nodal surface
We give a characterization of the generic projection on P2 of an algebraic surface of P3 with a finite number of nodes. The construction of an algebraic surface of P3 with a given number of nodes is thus equivalent to the construction of a plane curve with nodes and cusps in some special position.
Algebraic geometry
General
22
26
10.1007/s000140050074
http://www.ems-ph.org/doi/10.1007/s000140050074
A factorization of the Conway polynomial
J.
Levine
Brandeis University, WALTHAM, UNITED STATES
Conway polynomial, Alexander polynomial, link, knot, $\tilde\mu$ -invariants
It is shown that the Conway polynomial of a link is a product of two factors, the first of which is the Conway polynomial of a knot obtained by banding together the link components and the second is determined, via an explicit formula, by the $\tilde\mu$-invariants of the link. In particular we get a formula, in terms of the 7-invariants, for the first non-zero coefficient of the Conway polynomial. A similar formula is obtained for the multi-variable Alexander-polynomial.
Field theory and polynomials
General
27
53
10.1007/s000140050075
http://www.ems-ph.org/doi/10.1007/s000140050075
On nonpositively curved Euclidean submanifolds: splitting results
Luis
Florit
Estrada Dona Castorina 110, RIO DE JANEIRO RJ, BRAZIL
F.
Zheng
Ohio State University, COLUMBUS, UNITED STATES
Differential geometry
General
53
62
10.1007/s000140050076
http://www.ems-ph.org/doi/10.1007/s000140050076
Fundamental groups of compact manifolds and symmetric geometry of noncompact type
A.
Candel
California Institute of Technology, PASADENA, UNITED STATES
R.
Quiroga-Barranco
Cinestav, MEXICO, D.F., MEXICO
Differential geometry
General
63
83
10.1007/s000140050077
http://www.ems-ph.org/doi/10.1007/s000140050077
Spherical minimal immersions of the 3-sphere
G.
Toth
Rutgers University, CAMDEN, UNITED STATES
Wolfgang
Ziller
University of Pennsylvania, PHILADELPHIA, UNITED STATES
Differential geometry
General
84
117
10.1007/s000140050078
http://www.ems-ph.org/doi/10.1007/s000140050078
Multiplicity results for the two-vortex Chern-Simons Higgs model on the two-sphere
W.
DING
ACADEMIA SINICA, BEIJING, CHINA
Jürgen
Jost
Mathematik in den Naturwissenschaften, LEIPZIG, GERMANY
J.
LI
ACADEMIA SINICA, BEIJING, CHINA
G.
WANG
ACADEMIA SINICA, BEIJING, CHINA
Differential geometry
General
118
142
10.1007/s000140050079
http://www.ems-ph.org/doi/10.1007/s000140050079
On the dilatation of extremal quasiconformal mappings of polygons
Kurt
Strebel
, ZÜRICH, SWITZERLAND
Extremal qc mappings of disk, inscribed quadrilaterals and polygons
A polygon PN is the unit disk ${\Bbb D}$ with $n$ distinguished boundary points, $4\le n \le N$. An extremal quasiconformal mapping $f_0\: {\Bbb D}_z\to {\Bbb D}_w$ maps each polygon $P_N$ inscribed in ${\Bbb D}_z$ onto a polygon $P_N'$ inscribed in ${\Bbb D}_w$. Let fN be the extremal quasiconformal mapping of PN onto P'N. Let KN be its dilatation and let K0 be the maximal dilatation of f0. Then, evidently $\sup K_N\le K_0$. The problem is, when equality holds. This is completely answered, if f0 does not have any essential boundary points. For quadrilaterals Q and Q' = f0(Q) the problem is sup(M'/M) = K0, with M and M' the moduli of Q and Q' respectively.
Functions of a complex variable
General
143
149
10.1007/s000140050080
http://www.ems-ph.org/doi/10.1007/s000140050080
Approximating $\ell_2$-Betti numbers of an amenable covering by ordinary Betti numbers
B.
Eckmann
Eidgenössische Technische Hochschule, ZÜRICH, SWITZERLAND
Amenable groups, covering spaces, l 2 -homology, Betti numbers
It is shown that the $\ell_2$-Betti numbers of an amenable covering of a finite cell-complex can be approximated by ordinary Betti numbers of the finite Fmlner subcomplexes. This is a new proof, using simple homological arguments, of a recent result of Dodziuk and Mathai.
Algebraic geometry
General
150
155
10.1007/s000140050081
http://www.ems-ph.org/doi/10.1007/s000140050081
Platonic surface
R.
Brooks
Technion - Israel Institute of Technology, HAIFA, ISRAEL
Eigenvalue, Riemann surface, Ahlfors-Schwarz Lemma
If SO is a Riemann surface with a complete metric of finite area and constant curvature -1, let SC denote the conformal compactification of SO. We show that, under the assumption that the cusps of SO are large, there is a close relationship between the hyperbolic metrics on SO and SC. We use this relationship to show that $\liminf_{k \to \infty} \lambda_1(P_k) \ge 5/36$, where the Platonic surface Pk is the conformal compactification of the modular surface Sk.
Manifolds and cell complexes
General
156
170
10.1007/s000140050082
http://www.ems-ph.org/doi/10.1007/s000140050082