147 citations · 733 across the 37 of their papers we have counts for
37 papers
Dirac eigenvalues and the hyperspherical radius
Christian Baer
For closed connected Riemannian spin manifolds an upper estimate of the smallest eigenvalue of the Dirac operator in terms of the hyperspherical radius is proved. When combined wit…
First-order elliptic boundary value problems on manifolds with non-compact boundary
Christian Baer, Lashi Bandara
We consider first-order elliptic differential operators acting on vector bundles over smooth manifolds with smooth boundary, which is permitted to be noncompact. Under very mild as…
K-cowaist of manifolds with boundary
Christian Baer, Bernhard Hanke
We extend the K-cowaist inequality to generalized Dirac operators in the sense of Gromov and Lawson and study applications to manifolds with boundary.
Scalar curvature rigidity of warped product metrics
Christian Baer, Simon Brendle, Bernhard Hanke +1
We show scalar-mean curvature rigidity of warped products of round spheres of dimension at least 2 over compact intervals equipped with strictly log-concave warping functions. This…
Boundary conditions for scalar curvature
Christian Baer, Bernhard Hanke
Based on the Atiyah-Patodi-Singer index formula, we construct an obstruction to positive scalar curvature metrics with mean convex boundaries on spin manifolds of infinite K-area.…
Local Index Theory for Lorentzian Manifolds
Christian Baer, Alexander Strohmaier
Index theory for Lorentzian Dirac operators is a young subject with significant differences to elliptic index theory. It is based on microlocal analysis instead of standard ellipti…
The Faddeev-LeVerrier algorithm and the Pfaffian
Christian Baer
We adapt the Faddeev-LeVerrier algorithm for the computation of characteristic polynomials to the computation of the Pfaffian of a skew-symmetric matrix. This yields a very simple,…
Manifolds with many Rarita-Schwinger fields
Christian Baer, Rafe Mazzeo
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.…
Local Flexibility for Open Partial Differential Relations
Christian Baer, Bernhard Hanke
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 deriv…
Wave and Dirac equations on manifolds
Lars Andersson, Christian Baer
We review some recent results on geometric equations on Lorentzian manifolds such as the wave and Dirac equations. This includes well-posedness and stability for various initial va…
Boundary value problems for the Lorentzian Dirac operator
Christian Baer, Sebastian Hannes
On a compact globally hyperbolic Lorentzian spin manifold with smooth spacelike Cauchy boundary the (hyperbolic) Dirac operator is known to be Fredholm when Atiyah-Patodi-Singer bo…
The curl operator on odd-dimensional manifolds
Christian Baer
We study the spectral properties of curl, a linear differential operator of first order acting on differential forms of appropriate degree on an odd-dimensional closed oriented Rie…
A rigorous geometric derivation of the chiral anomaly in curved backgrounds
Christian Baer, Alexander Strohmaier
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 gravitati…
An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary
Christian Baer, Alexander Strohmaier
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 i…
Initial value problems for wave equations on manifolds
Christian Baer, Roger Tagne Wafo
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 sho…
Green-hyperbolic operators on globally hyperbolic spacetimes
Christian Baer
Green-hyperbolic operators are linear differential operators acting on sections of a vector bundle over a Lorentzian manifold which possess advanced and retarded Green's operators.…
Guide to Boundary Value Problems for Dirac-Type Operators
Christian Baer, Werner Ballmann
We present an introduction to boundary value problems for Dirac-type operators on complete Riemannian manifolds with compact boundary. We introduce a very general class of boundary…
Geometrically formal 4-manifolds with nonnegative sectional curvature
Christian Baer
A Riemannian manifold is called geometrically formal if the wedge product of any two harmonic forms is again harmonic. We classify geometrically formal compact 4-manifolds with non…
Some properties of solutions to weakly hypoelliptic equations
Christian Baer
A linear different operator L is called weakly hypoelliptic if any local solution u of Lu=0 is smooth. We allow for systems, that is, the coefficients may be matrices, not necessar…
Renormalized Integrals and a Path Integral Formula for the Heat Kernel on a Manifold
Christian Baer
We introduce renormalized integrals which generalize conventional measure theoretic integrals. One approximates the integration domain by measure spaces and defines the integral as…
Classical and Quantum Fields on Lorentzian Manifolds
Christian Baer, Nicolas Ginoux
We construct bosonic and fermionic locally covariant quantum field theories on curved backgrounds for large classes of fields. We investigate the quantum field and n-point function…
Boundary Value Problems for Elliptic Differential Operators of First Order
Christian Baer, Werner Ballmann
We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncompact, but the boundary is assumed to be compact. We r…
Linear Wave Equations on Lorentzian Manifolds
Christian Baer
This is a survey on the analytic theory of linear wave equations on globally hyperbolic Lorentzian manifolds. There is no claim of originality.
Stochastic completeness and volume growth
Christian Baer, G. Pacelli Bessa
It has been suggested in 1999 that a certain volume growth condition for geodesically complete Riemannian manifolds might imply that the manifold is stochastically complete. This i…