arXiv subjects

Bert Koehler

Publications and source records attributed to Bert Koehler.

4 recordsLinked to original sources

arXiv2021

Pointwise Properties of Fourier-Jacobi-Forms

Jacobi-Forms can be decomposed as a linear combination of Thetafunctions with modular forms as coefficients. It is shown that the space of these coefficient modular forms of Fourier-Jacobi-Forms, which come from Siegel cusp forms, has full rank in every point of the Satake boundary, if the index is 1, the weight is sufficiently large and the Satake boundary point has trivial stabilizer in $\Gamma_{n-1}$. This yields a local automorphic embedding of the Siegel modular variety. Klingen-Poincare series are the main tool. Despite of this richness it is proved that there are more Jacobi index 1 cusp forms than Fourier-Jacobi index 1 cusp forms for all sufficiently large weights extending a result of Dulinski.

math.NT↗

arXiv2021

Ergodic Density Estimates for some diffusion processes

For n-dimensional ergodic diffusion processes with values in $G=\mathbb{R}_{+}^n$ we prove time-independent upper bounds for the transitional density and so also for the unique ergodic density. We do not require geodesic completeness of the elliptic symbol towards the boundary of $G$.

math.PR↗

arXiv2007

On asymptotics of complete Ricci-flat Kähler metrics on open manifolds

Tian and Yau constructed a complete Ricci-flat Kähler metric on the complement of an ample and smooth anticanonical divisor. We inquire into the behaviour of this metric towards the boundary divisor and prove a slow decay rate of the difference to an appropriate explicitely given referential metric.

math.DG↗

arXiv2003

On invariance and Ricci-flatness of Hermitian metrics on open manifolds

We discuss a technique to construct Ricci-flat hermitian metrics on complements of (some) anticanonical divisors of almost homogeneous manifolds and discuss when this metric is complete and Kähler. This construction has a strong interplay with invariance groups of the same dimension as the manifold acting with an open orbit. Lie groups of this type we call divisorial. As an application we can describe compact manifolds admitting a divisorially invariant Kähler metric on an open subset. Finally, we see a connection between the reducibility of the anticanonical divisor and the non-triviality of the Kähler cone on the complement.

math.DG↗