Bemerkung über die Enveloppe einer Kugelfläche
The standard Berezin and Berezin-Toeplitz quantizations on a Kähler manifold are based on operator symbols and on Toeplitz operators, respectively, on weighted L2-spaces of holomorphic functions (weighted Bergman spaces). In both cases, the construction basically uses only the fact that these spaces have a reproducing kernel. We explore the possibilities of using other function spaces with reproducing kernels instead, such as L2-spaces of harmonic functions, Sobolev spaces, Sobolev spaces of holomorphic...
We use a Poincaré type formula and level set analysis to detect one-dimensional symmetry of stable solutions of possibly degenerate or singular elliptic equations of the formOur setting is very general and, as particular cases, we obtain new proofs of a conjecture of De Giorgi for phase transitions in and and of the Bernstein problem on the flatness of minimal area graphs in . A one-dimensional symmetry result in the half-space is also obtained as a byproduct of our analysis. Our approach...