arXiv subjects
Publications and source records attributed to Ilka Agricola.
In this paper we will prove new extrinsic upper bounds for the eigenvalues of the Dirac operator on an isometrically immersed surface $M^2 \hookrightarrow {\Bbb R}^3$ as well as intrinsic bounds for 2-dimensional compact manifolds of genus zero and genus one. Moreover, we compare the different estimates of the eigenvalue of the Dirac operator for special families of metrics.
We prove that the ring $\Aff{\R}{M}$ of all polynomials defined on a real algebraic variety $M\subset\R^n$ is dense in the Hilbert space $L^2(M,e^{-|x|^2}\deμ)$, where $\deμ$ denotes the volume form of $M$ and $\deν=e^{-|x|^2}\deμ$ the Gaussian measure on $M$.
We determine all Lie groups compatible with the gauge structure of the Standard Elementary Particle Model (SM) and their representations. The groups are specified by congruence equations of quantum numbers. By comparison with the experimental results, we single out one Lie group and show that this choice implies certain old and new correlations between the quantum numbers of the SM quantum fields as well as some hitherto unknown group theoretical properties of the Higgs mechanism.