@article{BaerHanke2022,
  author    = {B{\"a}r, Christian and Hanke, Bernhard},
  title     = {Local flexibility for open partial differential relations},
  series = {Communications on pure and applied mathematics / issued by the Courant Institute of Mathematical Sciences, New York Univ.},
  volume    = {75},
  journal   = {Communications on pure and applied mathematics / issued by the Courant Institute of Mathematical Sciences, New York Univ.},
  number    = {6},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {0010-3640},
  doi       = {10.1002/cpa.21982},
  pages     = {1377 -- 1415},
  year      = {2022},
  abstract  = {We show that local deformations, near closed subsets, of solutions to open partial differential relations can be extended to global deformations, provided all but the highest derivatives stay constant along the subset. The applicability of this general result is illustrated by a number of examples, dealing with convex embeddings of hypersurfaces, differential forms, and lapse functions in Lorentzian geometry. The main application is a general approximation result by sections that have very restrictive local properties on open dense subsets. This shows, for instance, that given any K is an element of Double-struck capital R every manifold of dimension at least 2 carries a complete C-1,C- 1-metric which, on a dense open subset, is smooth with constant sectional curvature K. Of course, this is impossible for C-2-metrics in general.},
  language  = {en}
}
@article{BaerMazzeo2021,
  author    = {B{\"a}r, Christian and Mazzeo, Rafe},
  title     = {Manifolds with many Rarita-Schwinger fields},
  series = {Communications in mathematical physics},
  volume    = {384},
  journal   = {Communications in mathematical physics},
  number    = {1},
  publisher = {Springer},
  address   = {Berlin},
  issn      = {0010-3616},
  doi       = {10.1007/s00220-021-04030-0},
  pages     = {533 -- 548},
  year      = {2021},
  abstract  = {The Rarita-Schwinger operator is the twisted Dirac operator restricted to 3/2-spinors. Rarita-Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare; it is even more unexpected for there to be large dimensional spaces of solutions. In this paper we prove the existence of a sequence of compact manifolds in any given dimension greater than or equal to 4 for which the dimension of the space of Rarita-Schwinger fields tends to infinity. These manifolds are either simply connected Kahler-Einstein spin with negative Einstein constant, or products of such spaces with flat tori. Moreover, we construct Calabi-Yau manifolds of even complex dimension with more linearly independent Rarita-Schwinger fields than flat tori of the same dimension.},
  language  = {en}
}
@article{BaerMoroianu2003,
  author    = {B{\"a}r, Christian and Moroianu, Sergiu},
  title     = {Heat kernel asymptotics for roots of generalized laplacians},
  year      = {2003},
  abstract  = {We describe the heat kernel asymptotics for roots of a Laplace type operator on a closed manifold. A previously known relation between the Wodzicki residue and heat trace asymptotics is shown to hold pointwise for the corresponding densities.},
  language  = {en}
}
@article{BaerPfaeffle2010,
  author    = {B{\"a}r, Christian and Pfaeffle, Frank},
  title     = {Asymptotic heat kernel expansion in the semi-classical limit},
  issn      = {0010-3616},
  doi       = {10.1007/s00220-009-0973-3},
  year      = {2010},
  abstract  = {Let H-h = h(2)L + V, where L is a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold and V is a symmetric endomorphism field. We derive an asymptotic expansion for the heat kernel of H-h as h SE arrow 0. As a consequence we get an asymptotic expansion for the quantum partition function and we see that it is asymptotic to the classical partition function. Moreover, we show how to bound the quantum partition function for positive h by the classical partition function.},
  language  = {en}
}
@unpublished{BaerPfaeffle2012,
  author    = {B{\"a}r, Christian and Pf{\"a}ffle, Frank},
  title     = {Wiener measures on Riemannian manifolds and the Feynman-Kac formula},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59998},
  year      = {2012},
  abstract  = {This is an introduction to Wiener measure and the Feynman-Kac formula on general Riemannian manifolds for Riemannian geometers with little or no background in stochastics. We explain the construction of Wiener measure based on the heat kernel in full detail and we prove the Feynman-Kac formula for Schr{\"o}dinger operators with bounded potentials. We also consider normal Riemannian coverings and show that projecting and lifting of paths are inverse operations which respect the Wiener measure.},
  language  = {en}
}
@article{BaerSchopka2003,
  author    = {B{\"a}r, Christian and Schopka, Sven},
  title     = {The dirac determinant of spherical space forms},
  year      = {2003},
  abstract  = {The zeta-regularized determinants of the Dirac operator and of its square are computed on spherical space forms. On S^2 the determinant of Dirac operators twisted by a complex line bundle is also calculated.},
  language  = {en}
}
@article{BaerStrohmaier2019,
  author    = {B{\"a}r, Christian and Strohmaier, Alexander},
  title     = {An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary},
  series = {American Journal of Mathematics},
  volume    = {141},
  journal   = {American Journal of Mathematics},
  number    = {5},
  publisher = {Johns Hopkins Univ. Press},
  address   = {Baltimore},
  issn      = {0002-9327},
  doi       = {10.1353/ajm.2019.0037},
  pages     = {1421 -- 1455},
  year      = {2019},
  abstract  = {We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by the same expression as in the index formula of Atiyah-Patodi-Singer for Riemannian manifolds with boundary. The index is also shown to equal that of a certain operator constructed from the evolution operator and a spectral projection on the boundary. In case the metric is of product type near the boundary a Feynman parametrix is constructed.},
  language  = {en}
}
@article{BaerStrohmaier2016,
  author    = {B{\"a}r, Christian and Strohmaier, Alexander},
  title     = {A Rigorous Geometric Derivation of the Chiral Anomaly in Curved Backgrounds},
  series = {Communications in mathematical physics},
  volume    = {347},
  journal   = {Communications in mathematical physics},
  publisher = {Springer},
  address   = {New York},
  issn      = {0010-3616},
  doi       = {10.1007/s00220-016-2664-1},
  pages     = {703 -- 721},
  year      = {2016},
  abstract  = {We discuss the chiral anomaly for a Weyl field in a curved background and show that a novel index theorem for the Lorentzian Dirac operator can be applied to describe the gravitational chiral anomaly. A formula for the total charge generated by the gravitational and gauge field background is derived directly in Lorentzian signature and in a mathematically rigorous manner. It contains a term identical to the integrand in the Atiyah-Singer index theorem and another term involving the.-invariant of the Cauchy hypersurfaces.},
  language  = {en}
}
@article{BaerWafo2015,
  author    = {B{\"a}r, Christian and Wafo, Roger Tagne},
  title     = {Initial value problems for wave equations on manifolds},
  series = {Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics},
  volume    = {18},
  journal   = {Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics},
  number    = {1},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {1385-0172},
  doi       = {10.1007/s11040-015-9176-7},
  pages     = {29},
  year      = {2015},
  abstract  = {We study the global theory of linear wave equations for sections of vector bundles over globally hyperbolic Lorentz manifolds. We introduce spaces of finite energy sections and show well-posedness of the Cauchy problem in those spaces. These spaces depend in general on the choice of a time function but it turns out that certain spaces of finite energy solutions are independent of this choice and hence invariantly defined. We also show existence and uniqueness of solutions for the Goursat problem where one prescribes initial data on a characteristic partial Cauchy hypersurface. This extends classical results due to Hormander.},
  language  = {en}
}
@article{BaerenzungHolschneiderLesur2016,
  author    = {B{\"a}renzung, Julien and Holschneider, Matthias and Lesur, Vincent},
  title     = {constraints},
  series = {Journal of geophysical research : Solid earth},
  volume    = {121},
  journal   = {Journal of geophysical research : Solid earth},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9313},
  doi       = {10.1002/2015JB012464},
  pages     = {1343 -- 1364},
  year      = {2016},
  abstract  = {Prior information in ill-posed inverse problem is of critical importance because it is conditioning the posterior solution and its associated variability. The problem of determining the flow evolving at the Earth's core-mantle boundary through magnetic field models derived from satellite or observatory data is no exception to the rule. This study aims to estimate what information can be extracted on the velocity field at the core-mantle boundary, when the frozen flux equation is inverted under very weakly informative, but realistic, prior constraints. Instead of imposing a converging spectrum to the flow, we simply assume that its poloidal and toroidal energy spectra are characterized by power laws. The parameters of the spectra, namely, their magnitudes, and slopes are unknown. The connection between the velocity field, its spectra parameters, and the magnetic field model is established through the Bayesian formulation of the problem. Working in two steps, we determined the time-averaged spectra of the flow within the 2001-2009.5 period, as well as the flow itself and its associated uncertainties in 2005.0. According to the spectra we obtained, we can conclude that the large-scale approximation of the velocity field is not an appropriate assumption within the time window we considered. For the flow itself, we show that although it is dominated by its equatorial symmetric component, it is very unlikely to be perfectly symmetric. We also demonstrate that its geostrophic state is questioned in different locations of the outer core.},
  language  = {en}
}
@article{Boeckmann1996,
  author    = {B{\"o}ckmann, Christine},
  title     = {Curve fitting and identification of physical spectra},
  year      = {1996},
  language  = {en}
}
@article{Boeckmann1996,
  author    = {B{\"o}ckmann, Christine},
  title     = {Curve fitting and identification of physical spectra},
  year      = {1996},
  language  = {en}
}
@article{Boeckmann1995,
  author    = {B{\"o}ckmann, Christine},
  title     = {A modification of the trust-region Gauss-Newton method to solve separable nonlinear least squares problems},
  year      = {1995},
  language  = {en}
}
@article{Boeckmann1997,
  author    = {B{\"o}ckmann, Christine},
  title     = {Projection method for lidar measurements},
  isbn      = {981-02-2918-6},
  year      = {1997},
  language  = {en}
}
@book{Boeckmann1992,
  author    = {B{\"o}ckmann, Christine},
  title     = {A modification of the Trust-Region Gauss-Newton method to solve separable nonlinear least squares problems},
  series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  volume    = {1992, 17},
  journal   = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {14 Bl.},
  year      = {1992},
  language  = {en}
}
@book{Boeckmann1992,
  author    = {B{\"o}ckmann, Christine},
  title     = {Curve fitting and identification of physical spectra},
  series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  volume    = {1992, 18},
  journal   = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {17 Bl.},
  year      = {1992},
  language  = {en}
}
@article{Boeckmann2000,
  author    = {B{\"o}ckmann, Christine},
  title     = {Evaluation of Multi-spectral Lidar Measurements of the Tropo- and Stratosphere via Modern Mathematical Methods for Inverse III- posed Problems to Determine the Aerosol Size Distribution},
  year      = {2000},
  language  = {en}
}
@article{BoeckmannBernutatFischer1998,
  author    = {B{\"o}ckmann, Christine and Bernutat, Claudia and Fischer, Silva},
  title     = {The nonlinear LIDAR-equation : an inverse ill-posed problem},
  year      = {1998},
  language  = {en}
}
@article{BoeckmannBieleNeuber1998,
  author    = {B{\"o}ckmann, Christine and Biele, Jens and Neuber, Roland},
  title     = {Analysis of multi-wavelength lidar data by inversion with mollifier method},
  year      = {1998},
  language  = {en}
}
@unpublished{BoeckmannBieleNeuberetal.1997,
  author    = {B{\"o}ckmann, Christine and Biele, Jens and Neuber, Roland and Niebsch, Jenny},
  title     = {Retrieval of multimodal aerosol size distribution by inversion of multiwavelength data},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14360},
  year      = {1997},
  abstract  = {The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, the points r where n(r) is evaluated may be freely selected. A new twodimensional model for the troposphere is proposed.},
  language  = {en}
}