FORSCHUNGSBERICHT 1999-2001

INDEX

Institut für Angewandte Mathematik, Abt. f. Funktionalanalysis u. Numerische Mathematik

Forschungsbericht

Mathematisch-Naturwissenschaftliche Fakultät

Mathematisches Institut der Universität Bonn

Allgemeine Angaben:
Beringstraße 1, 53115 Bonn
Telefon: 0228 / 73-2204
Fax: 0228 / 73-7916
eMail: herchen@math.uni-bonn.de
WWW: http://www.math.uni-bonn.de

Hauptamtliche Professoren:
Prof. Dr. Werner Ballmann
Prof. Dr. Carl-Friedrich Bödigheimer
Prof. Dr. Egbert Brieskorn
Stud. Prof. Dr. Paul Bungartz
Prof. Dr. Jens Franke
Prof. Dr. Ursula Hamenstädt
Prof. Dr. Günter Harder
Prof. Dr. Stefan Hildebrandt
Prof. Dr. Hermann Karcher
Prof. Dr. Peter Koepke
Prof. Dr. Ingo Lieb
Prof. Dr. Werner Müller
Prof. Dr. Florian Pop
Prof. Dr. Werner Raab
Prof. Dr. Rainer Schätzle
apl. Prof. Gerd Schmalz

Wissenschaftliches Personal:
Universitätsstellen
Dr. Ludwig Balke
Dr. Vincente Cortes-Suarez
Dr. Claus Hertling
Dr. Christian Kaiser
Dr. Peter Klein
Dr. Kai Köhler
Dr. Karl Leschinger
Dr. Benedikt Löwe
Dr. Lan Ma
Dr. Heiko Mosel von der
Dr. Birgit Richter
Dr. Alois Scharf-Knappe
Dr. Bernd Schmidt
Dr. Dorothee Schüth
Dr. Bernd Steinert
Dr. Matthias Weber
Dr. Gregor Weingart
Dr. Daniel Wienholtz

Stipendiaten
Pawel Strzelecki 2 Jahre, 1999-2001 (Alexander von Humboldt-Stiftung, Hildebrandt, S.)

Forschungsschwerpunkte:
Kombinatorik von Pflasterungen
(Balke L.)

Riemansche Geometrie, Geodätische Flüsse, Brownsche Bewegung, Geometrie simplizialer Komplexe, Dirac und Lpalaceoperatoren
(Ballmann W.)

Operaden
(Bödigheimer, C.-F., Richter, B.)

Modulräume Riemannscher Flächen, Algebraische Approximationstheorie von Funktoren
(Bödigheimer C.-F.)

Die Biographie und das Werk Felix Hausdorffs
(Brieskorn E., Purkert W.)

Differentialgeometrie
(Cortés V.)

Differentialgeometrie
(Cortez V.)

Algebra, diophantische Geometrie
(Franke J.)

Differentialgeometrie, Minimalflächen, H-Flächen
(Große-Brauckmann C., Karcher H., Weber M.)

Geometrie und Dynamik negativ gekrümmter Mannigfaltigkeiten, Teichmüllertheorie
(Hamenstädt U.)

Arithmetik
(Harder G.)

Komplexe Analysis
(Hefer, T.)

Analytische Invarianten und Modulräume von Singularitäten
(Hertling C.)

Variationsrechnung, partielle Differentialgleichungen
(Hildebrandt S.)

Shimura Carietäten, Fundamentales Lemma
(Kaiser Ch.)

Minimale Untermannigfaltigkeiten, Qualitative Riemannsche Geometrie, Mathematische Visualisierung
(Karcher, H.)

Kleinsche Gruppen
(Kleineidam G., Souto J.)

Axiomatische Mengenlehre, große Kardinalzahlen
(Koepke P.)

Komplexe Analysis, Cauchy-Riemannsche Differentialgleichungen, Integralformeln
(Lieb I.)

Globale Analysis
(Müller W., Köhler K., Sick O.)

Fundamentalgruppe von Kurven, Anabelsche Geometrie
(Pop, F., Saidi, M.)

Regularität von Varifaltigkeiten, Regularität für den Mittleren Krümmungsfluß, Willmore-Funktional und -Fluß, Phasenfeldgleichungen u. Stefanprobleme, Konvex Geometrie
(Schätzle R.)

Abbildungen von CR-Mannigfaltigkeiten, Normalformen, Cartansche Zusammenhänge
(Schmalz G.)

Isospektrale Mannigfaltigkeiten
(Schüth D.)

Nenner von Eisenstein-Kohomologie-Klassen
(Steinert B.)

Empirische Unterrichtsforschung im OECD-PISA_Projekt
(Wynands A.)

Besondere Forschungsförderung:
Bonner Internationale Graduiertenschule in Mathematik, Physik, und Astronomie seit 10/2001
(Bödigheimer, C.-F., Sprecher)

DFG-Projekt: Spezielle geometrische Strukturen in der Stringtheorie im Rahmen des DFG-Schwerpunktprogramms 1096: Stingtheorie im Kontext von Teilchenphysik, Quantenfeildtheorie, Quantengravitation, Kosmologie und Mathematik.
(Projektleiter seit Sept.2000: Cortez, V.)

Europäisches Netzwerk ANACOGA
(Lieb, I.)

Hausdorf Edition
(Mathematisches Institut der Universität Bonn, Prof. Dr. E. Brieskorn, DFG)

Post-Doc am Institut Genoble
(Hefer, T.)

SFG 256, Graduierten Kolleg, siehe dort

TMR-Projekt: Parabolic equations, Netzwerk 7 europäischer Länder, Koordinator für Deutschland für das Jahr 2001.
(Schätzle, R.)

Veröffentlichungen:

Ballman, W., Brin, M.
Diameter rigidity of sperical polyhedra
Duke Math. J. 97, (1999), pp. 235-259

Ballmann, W.
The Matin boundary of certain Hadamard manifolds. Proceedings on Analysis and Geometry.
Sobolev Institute Press, Novosibirsk, (2000)

Ballmann, W., Brin, M.
Rank rigidity of Euclidean polyhedra
Amer. J. Math. 122 (2000), pp. 873-885

Ballmann, W., Brüning, J.
On the spectral theory of manifolds with cusps.
J. Math. Pures Appl. 80, (2001), pp. 593-625, Jahresberichte DMV 103

Ballmann, W., Swiatkowski, J.
On groups acting on nonpositively curved cubical complexes.
L'Enseigenement Math. 45, (1999), pp. 51-81

Bödigheimer, C.-F., Tillman, U.
Stripping and splitting of decorated mapping class groups.
In: Cohomological Methods in Homotopy Theory, Proc. Barcelona 1998, Birkhäuser, Prograss in Math. 196, (2001), 47-57

Bödigheimer, C.-F., Cohen, F.R., Peim, M.D.
Mapping class groups and function spaces. Homotopy methods in algebraic topology.
In: Homotopy Methods in Algebraic Topology, Contemp. Math. 271, (2001), 17-39

Cortez, V.
A new construction of homogenous quaternionic manfiolds and related geometric structures.
Memoirs Amer. Math. Soc. 147, No. 700, (2000), pp. 1-63

Cortez, V.
Special Kähler manifolds: a survey.
Rend. Circ. Mat. Palermo (2) Suppl. no.66, (2001)

Cortez, V., Alekseevsky, D.V.
Classification of stationary compact homogenous special pseudo Kähler manifolds of semisimple group.
Proc. London Math. Soc. (3), (2000), pp. 211-230

Cortez, V., Alekseevsky, D.V.
Classification of indefinite hyper-Kähler symmetric spaces.
Asian J. Math. 5, no. 4, (2001), pp. 663-64

Cortez, V., Baues, O.
Realisation of special Kähler manifolds as parabolic speres.
Proc. Amer. Math. Soc. 129, no. 8, (2001), pp. 2403-2407

Corzez, V., Alekseevsky, D.V.
Isometry groups of homogenous quaterionic Kähler manfiolds.
J. Geom. Anal. 9, no.4, (1999), pp. 513-545

Franke, J.
On the singularities of residual Eisenstein series.
Inv. Math. 138, no. 2, (1999), pp. 307-317

Franke, J.
On the Brown representability theorem for triangulated categories.
Topology 40, no. 4, (2001), pp. 667-680

Hamenstädt, U.
Cocycles, symplectic structures and intersection.
GADA 9, (1999), pp. 90-140

Hamenstädt, U.
New Examples of maximal surfaces.
L'Enseignement Math. 47, (2001), pp. 65-101

Harder, G.
Galoismoduln und Shimura-Varietäten.
Jber. d. Dt. Math.-Verein. 101, (1999), pp. 26-46

Hefer, T.
Regularität von Randwerten der kanonischen Lösung der sigma-Gleichung auf streng pseudokonkaven Gebieten.
Bonner Math. Schriften, 320, (1999), 126 S.

Hildebrandt, S.
Reine oder Angewandte Mathematik, Mathemtische Semesterberichte 47

Hildebrandt, S., Lax, P.D.
Otto Toeplitz.
Bnner Mathem. Schriften, (1999), Nr. 319, Bonn

Hildebrandt, S., Mosel von der, H.
On two dimensional parametric variational problems.
Cal.Var. 9, (1999), pp. 249-267

Hildebrandt, S., Sauvigny, F.
Minimal surfaces in a wedge III. Existence of graph solutions and some uniqueness results.
J. reine und angew. Math. 514, (1999), pp. 71-101

Hildebrandt, S., Sauvigny, F.
Minimal surfaces in a wedge IV. Hölder estimates of the Gauss map and a Bernstein theorem.
Cal.Var. 8, (1999), pp. 71-99

Hirzebruch, F.
Complex cobordism and the elliptic genus.
Notes by Adrian Langer. Contemp. Math., 241, Algebraic geometry:Hirzebruch 70 (Warsaw, 1998), (1999), pp. 9-20, Amer. Math. Soc., Prodvidence, RI

Hirzebruch, F., Ciliberto, C.F., Miranda R., Teicher M.
Applications of algebraic geometry to coding theory, physics and computation. Proceedings of the NATO Advanced Research Workshop held in Eilat,
NATO Science Series II: Mathematics, Physics and Chemistry, 36.Kluwer Academic Pulishers, Dordrecht, (2001), pp. 337 pp.

Kaiser, C., Riedel, J.-E.
Tamagawazahlen und die Poincar\'ereihen affiner Weylgruppen.
J. Reine Angew. Math. 519, (2000), pp. 31-39

Karcher, H.
Submersions via Projections.
Geometria Dedicata 74, (1999), pp. 249-279

Karcher, H., Hoffmann, H. , Wei, F.
The singly periodic genus-One helicoid.
Comment Math. Helv. 74, (1999), pp. 248-279

Klingenberg, W.
Real hypersurfaces in Kähler manifolds.
Asian J. Math. 5, no.1, (2001), pp. 1-17

Klingenberg, W., Huisken, G.
Flow of real hypersurfaces by the traced of the Levi form.
Math. Res. Lett. 6, no.5-6, (1999), pp. 645-661

Koepke, P.
An iteration model violating the sinular cardinals hypothesis. Sets and proofs (Leeds, 1997)
95-102, London Math. Soc. Lecture Note Ser., 258, Cambridge Univ. Press, Cambridge, (1999)

Lieb, I., Hefer, T.
On teh compactness of the sigmal-Neumann operator.
Ann. Fac. Sci. Toulouse 9, (2000), pp. 415-432

Lieb, I., Michel, J.
The Cauchy-Riemann complex.
Vieweg Braunschweig/Wiesbaden, (2001), 362p.

Löwe, B.
Turing cones and set theory of the reals.
Arch. Math. Logic 40, no.8, (2001), pp. 651-666

Löwe, B.
Revision sequences and computers with an infinite amount of time. Essays on non-classical logic.
(Konstanz, 1999), 37-59, Adv. Log., 1, World Sci.Publishing, River Edge, NJ, (2001)

Löwe, B.
A first glance at non-restrictiveness.
Philos. Math. (3) 9, no.3, (2001), pp. 347-354

Löwe, B.
Revision sequences and computers with an infinite amount of time.
J. Logic Comput. 11, no. 1, (2001), pp. 25-40

Löwe, B., Brendle, J.
Solovay-type characterizations for forcing-algebras.
J. Symbolic Logic 64, no.3, (1999), pp. 1307-1323

Löwe, B., Gitik, M.
Cofinalities of linear orders.
Order 16 (1999), no.2, (2000), pp. 105-111

Löwe, B., Halbeisen, L.
Techniques for approching the dual Ramsey property in the projective hierarchy.
Pacific J. Math. 200, no.1, (2001), pp. 119-145

Löwe, B., Halbeisen, L.
Ultrafilter spaces on the semilattice of partitions.
Topology Appl. 115, no.3, (2001), pp. 317-333

Lytchak, A., Charney, R.
Metric characterizations of sperical and Euclidean buildings.
Geom. Topol. 5, (2001)

Mosel von der, H.
Elastic Knots in Euclidean 3-Space.
Annales de l'I.H.P., Analyse non lineaire 16 no.2, (1999), pp. 137-166

Mosel von der, H., Clarezn, U.
Compactness Theorems and an Isoperimetric Inequality for Critical Points of Elliptic Parametric Functionals.
Calc. Var 13, (2001), pp. 85-107

Müller, W.
On the singularities of residual intertwining operators.
Geom. funct. anal. 10, (2000), pp. 1118-1170

Müller, W.
Automorphe Formen und L-Funktionen.
In: 100 Jahre Beliner Mathematische Gesellschaft, Festschrift, Herausgegeben von BMG, Berlin 2001, S. 31-66

Pop, F.
Alterations and birational anabelian geometry. Resolution of singularities (Obergurg, 1997)
Progr. Math., 181, Birkhäuser, Basel, (2000), pp. 519-532

Richter, B.
$E_ \infty$-structures for $Q_*(R)$.
Mathematische Annalen, 316, (2000), 547-564

Richter, B.
Taylor towers of $\Gamma$-modules.
Annales de L'Institut Fourier,tome 51, fascicule 4, (2001), pp. 995-1023

Richter, B., Pirashvili, T.
Robinson-Whitehouse complex and stable homotopy.
Topology 39, no.3, (2000), pp. 525-530

Schätzel, R., Kuwert, E.
The Willmore Flow with small initial energy.
Journal Differential Geometry, 57, (2001), pp. 409-441

Schätzle, R.
On the perturbaion of the zeros of complex polynomials.
IMA Journal of Numerical Analysis, 20, (2000), pp. 185-202

Schätzle, R.
The quasi-stationary phase field equations with Neumann boundary conditions.
Journal of Differential Equations, 162, No.2, (2000), pp. 473-503

Schätzle, R., Canarius, F.
Multiple solutions for a semilinear elliptic problem.
Nonlinear Analysis TMA, Ser.A: Theory Methods, 45, no.7, (2001), pp. 937-956

Schätzle, R., Henry, M., Hilhorst, D.
Convergence to a viscosity solution for an advection-reaction-diffusion equation arising from a chemotaxis-growth model.
Hiroshima Mathematical Journal, Vol. 29, No.3, (2000), pp. 591-630

Schätzle, R., Hilhorst, D., Logak, E.
Global existence for a nonlocal mean curvature flow as a limit of a parabolic-elliptic phase transition model.
Interfaces and Free Bondaries, 2, (2000), pp. 267-282

Schätzle, R., Hug, D.
Intersections and tranlative integral formulas for boundaries of convex bodies.
Mathematische Nachrichten, 226, (2001), pp. 99-128

Schätzle, R., Kratz, W., Liebscher, D.
On the definiteness of quadratic functionals.
Annali di Mathematica Pura ed Applicata, IV, Vol. CLXXVI, (1999), pp.133-143

Schätzle, R., Nakamura, K.I., Matano, H., Hilhorst, D.
Singular limit of a reaction-diffusion equation with a spatially inhomogeneous reaction term.
Journal of Statictical Physics, Vol. 95, No.5/6, (1999), pp.1165-1185

Schätzle, R., Stoth, B.
The stationary mean field model of superconductivity: Partial regularity of the free boundary.
Journal of Differential Equations, 157, (1999), pp. 319-328

Schätzle, R., Styles, V.
Analysis of a Mean Model of Superconducting Vortices.
European Journal of Applied Mathematics, 10, (1999), pp. 319-352

Schmalz, G.
Remarks on CR-manifolds of codimension 2 in $\bbC^4$
Rend. Circ. Math. Palermo (2), Suppl. 59 (1999), 171-180

Schmalz, G., Ezov, V.
Infinitesimale Starrheit hermitescher Quadriken in allgemeiner Lage.
Mathematische Nachrichten 204, (1999), 41-60

Schmalz, G., Ezov, V.
Triviality problem for nil-isotropic automorphisms on non-quadratic CR-manfiolds.
Bonner Mathematische Schriften 338, Bonn 2001

Schmalz, G., Ezov, V.
Holomorphe Klassifizierung der CR-Mannigfaltigkeiten mit starrer Leviform (auf Russisch).
In: Komplexe Analysis in der modernen Mathematik. Zum 80. Geburtstag von B.V. Shabat, Moskau, Fazis, 2001, 99-122

Schmalz, G., Ezov, V., Isaev, A.
Invariants of elliptic and hyperbolic CR-Structures of codimension 2.
In: Int. J. Math., 10:1 (1999), 1-52

Schmalz, G., Ezov, V., Loboda, A.
Canonical form of the 4th order polynomial in the normal equation of a real hypersurface in $\bbC^3$ (auf Russisch).
Mat. zametki (Math. Notes) 66:4 (1999), 624-626

Schmalz, G., Slovak, J.
The geometry of hyperbolic and elliptic CR-manifolds of codimension two.
Asian J. Math. 4:3, (2000), pp. 565-598

Schülth, D.
Continuous families of isospectral metrics on simply connected manifolds.
Annals of Mathematics, 149, (1999), pp. 237-308

Schüth, D.
Isospectral metrics on five-dimensional sheres.
J. Differential Geometry, 58, (2001), pp. 87-111

Schüth, D.
Isospectral manifolds with different local geometries.
J. reine angew. Math., 534, (2001), pp. 41-94

Wörmann, T., Berr, R.
Positive polynomials on compact sets.
Manuscripta mathematica, abstract Volume 104 Issue 2, (2001), pp. 135-143

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