Publications of Daniel Grieser

Publications of Daniel Grieser

Abstracts for many of the research publications can be found here.

Research papers / Forschungsarbeiten

  • Spectral geometry on manifolds with fibred boundary metrics I: Low energy resolvent (with M. Talebi and B. Vertman), Preprint (2020), arXiv.
  • The Calderón Projector for Fibred Cusp Operators (with K. Fritzsch and E. Schrohe), Preprint (2020), arXiv.
  • Scales, blow-up and quasimode constructions, in: Geometric and Computational Spectral Theory, A. Girouard et al, eds, Contemp. Math. 700, AMS, 207-266 (2017), arXiv.
  • Soliton transport in tubular networks: Transmission at vertices in the shrinking limit (with H. Uecker, Z. Sobirov, D. Babajanov, Doniyor and D. Matrasulov), Phys. Rev. E 91 (2015), Doi 10.1103/PhysRevE.91.023209. Paper, arXiv.
  • The exponential map at a cuspidal singularity (with V. Grandjean), Journal für die reine und angewandte Mathematik (Crelles Journal) (2015), 1-35. DOI: 10.1515/crelle-2015-0020, arXiv.
  • A new simple proof of the Aztec diamond theorem (with M. Fendler), Graphs and Combinatorics (2015), 1-7. DOI: 10.1007/s00373-015-1663-x, arXiv, read online.
  • A Parametrix Construction for the Laplacian on Q-rank 1 Locally Symmetric Spaces (with E. Hunsicker), Proceedings of the Workshop on Fourier Analysis and Pseudo-Differential Operators, Aalto, Finland. Trends in Mathematics, Birkhäuser, Basel 2014. arXiv.
  • The plasmonic eigenvalue problem, Rev. Math. Phys. 26, 1450005 (2014) (26 pp.) DOI: 10.1142/S0129055X14500056arXiv.
  • Hearing the shape of a triangle (with S. Maronna), Notices of the American Mathematical Society 60 (12/2013), 1440-1447. Paper, arXiv.
  • Monotone unitary families, Proc. Amer. Math. Soc. 141 (2013), 997-1005. DOI: 10.1090/S0002-9939-2012-11552-7, arXiv.
  • A natural differential operator on conic spaces, Discrete Contin. Dyn. Syst. (8th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Dresden 2010), 2011, p. 568-577. Paper.
  • Perturbation theory for plasmonic eigenvalues (with S.-A. Biehs, M. Holthaus, O. Huth, F. Rüting, and H. Uecker), Phys. Rev. B 80 (2009), 245405 (8pp). DOI:  10.1103/PhysRevB.80.245405, paper.
  • Surface plasmon resonances of an arbitrarily shaped nanoparticle: High frequency asymptotics via pseudo-differential operators (with F. Rüting), J. Phys. A: Math. Theor. 42 135204 (6pp)   doi: 10.1088/1751-8113/42/13/135204, arXiv.
  • Pseudodifferential operator calculus for generalized Q-rank 1 locally symmetric spaces, I (with E. Hunsicker), Journal of Functional Analysis 257 (2009), pp. 3748-3801. DOI: 10.1016/j.jfa.2009.09.016, arXiv.
  • Asymptotics of eigenfunctions on plane domains (with D. Jerison), Pacific J. of Mathematics 240 (2009), 109-133. DOI: 10.2140/pjm.2009.240.109, arXiv.
  • Thin tubes in mathematical physics, global analysis and spectral geometry, in: Analysis on Graphs and its Applications. Proceedings of Symposia in Pure Mathematics, P. Exner, J. Keating, P. Kuchment, T. Sunada, and A. Teplyaev (eds.), AMS, 2008, 565-594. arXiv.
  • Spectra of graph neighborhoods and scattering, Proceedings of the London Mathematical Society 97 (2008), 718-752. arXiv.
  • Geodesics on singular surfaces, Oberwolfach Reports No. 41/2007. Paper, full volume.
  • The first eigenvalue of the Laplacian, isoperimetric constants, and the Max Flow Min Cut Theorem, Archiv der Mathematik 87 (2006), 75-85. Paper.
  • Cheeger's inequality revisited, Oberwolfach Reports No. 39/2005. Paper, full volume.
  • Local geometry of singular real analytic surfaces, Trans. Amer. Math. Soc.355 (2003), 1559-1577. DOI: 10.1090/S0002-9947-02-03168-9, arXiv.
  • On the L^2-Stokes theorem and Hodge theory for singular algebraic varieties (with M. Lesch), Math. Nachr. 246-247 (2002), 68-82. Paper.
  • Quasiisometry of singular metrics, Houston J. Math 28 (2002), 741-752. Paper.
  • Uniform bounds for eigenfunctions of the Laplacian on compact manifolds with boundary, Comm. PDE 27 (2002), 1283-1299. Paper.
  • Singular asymptotics lemma and Push-forward theorem (with M. Gruber), in J.B.Gil et al. (eds.), Approaches to Singular Analysis, 117-130, Operator Theory: Advances and Applications, 125. Advances in Partial Differential Equations, Birkhäuser, Basel, 2001. Paper.
  • Basics of the b-calculus, in J.B.Gil et al. (eds.), Approaches to Singular Analysis, 30-84, Operator Theory: Advances and Applications, 125. Advances in Partial Differential Equations, Birkhäuser, Basel, 2001. Paper.
  • The free boundary problem in the optimization of composite membranes (with S. Chanillo and K. Kurata), in: Differential Geometric Methods in the Control of Partial Differential Equations, R. Gulliver et al. (eds), Cont. Math. 268 (2000), 61-81. Paper.
  • Symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes (with S. Chanillo and K. Kurata - on the theory, and M. Imai and I. Ohnishi - on the numerics), Comm. Math. Physics 214 (2000), 315-337. DOI: 10.1007/PL00005534, arXiv.
  • The size of the first eigenfunction of a convex planar domain (with D. Jerison), Journal of the AMS 11 (1998), 41-72. Paper.
  • Asymptotics of the first nodal line of a convex domain (with D. Jerison), Inventiones Math. 125 (1996), 197-219. Paper.
  • Asymptotics of the first nodal line (with D. Jerison), in "Journees Equations aux derivees partielles'' St-Jean-de-Monts 1995. Paper.
  • Counting complements in the partition lattice, and hypertrees, J.Comb.Th.A 57 (1991), 144-150. DOI: 10.1016/0097-3165(91)90012-6, paper.
  • Some results on the complexity of families of sets, Disc.Math. 88 (1991), 179-192. DOI: 10.1016/0012-365X(91)90008-P, paper.
  • Hook-free colorings and a problem of Hanson (with M. Aigner), Combinatorica 8(2) (1988), 143-148. DOI: 10.1007/BF02122795, paper.
  • On the representing number of intersecting families (with M. Aigner and P. Erdös), Arch.Math. 49 (1987), 114-118. DOI: 10.1007/BF01200473, paper.

Papers related to teaching / Didaktische Arbeiten

Theses / Qualifizierungsarbeiten

Books edited / Herausgegebene Bücher

  • Microlocal Methods in Mathematical Physics and Global Analysis (with S.Teufel und A.Vasy), Trends in Mathematics / Research Perspectives, Birkhäuser Verlag, Basel, 2012.

  • Approaches to Singular Analysis (with J.Gil and M.Lesch), Operator Theory: Advances and Applications, 125. Advances in Partial Differential Equations, Birkhäuser Verlag, Basel, 2001.

Textbooks / Lehrbücher

Publications directed at a general mathematical audience (in particular students) / Allgemeine mathematische Publikationen (auch für Studenten)

Mathematics related publications for a general audience / Allgemeine Publikationen

(Stand: 26.09.2020)