Comparison of the Bergman kernel and the Carath\'eodory--Eisenman volume

It is proved that for any domain in $\mathbb C^n$ the Caratheodory--Eisenman volume is comparable with the volume of the indicatrix of the Caratheodory metric up to small/large constants depending only on $n.$ Then the "multidimensional Suita conjecture" theorem of Blocki and Zwonek implies a comparable relationship between these volumes and the Bergman kernel.Comment: 5 page

"Convex" characterization of linearly convex domains

We prove that a $C^{1,1}$-smooth bounded domain $D$ in \C^n is linearly convex if and only if the convex hull of any two discs in $D$ with common center lies in $D.$Comment: to appear in Math. Scand.; v3: Appendix is adde

Rigid characterizations of pseudoconvex domains

We prove that an open set $D$ in \C^n is pseudoconvex if and only if for any $z\in D$ the largest balanced domain centered at $z$ and contained in $D$ is pseudoconvex, and consider analogues of that characterization in the linearly convex case.Comment: v2: Proposition 14 is improved; v3: Example 15 and the proof of Proposition 14 are change

Discontinuity of the Lempert function and the Kobayashi--Royden metric of the spectral ball

Some results on the discontinuity properties of the Lempert function and the Kobayashi pseudometric in the spectral ball are given.Comment: After submitting this paper to a journal in January the authors received a paper by G. Bharali (see arXiv:0704.1966), where some of the problems are similar to that in our pape

New methods in conformal partial wave analysis

We report on progress concerning the partial wave analysis of higher correlation functions in conformal quantum field theory.Comment: 16 page

On the zero set of the Kobayashi--Royden pseudometric of the spectral unit ball

Given $A\in\Omega_n,$ the $n^2$-dimensional spectral unit ball, we show that $B$ is a "generalized" tangent vector at $A$ to an entire curve in $\Omega_n$ if and only if $B$ is in the tangent cone $C_A$ to the isospectral variety at $A.$ In the case of $\Omega_3,$ the zero set of this metric is completely described.Comment: minor changes; to appear in Ann. Polon. Mat

Refined physical properties and g',r',i',z',J,H,K transmission spectrum of WASP-23b from the ground

Multi-band observations of planetary transits using the telescope defocus technique may yield high-quality light curves suitable for refining the physical properties of exoplanets even with small or medium size telescopes. Such observations can be used to construct a broad-band transmission spectrum of transiting planets and search for the presence of strong absorbers. We have thoroughly characterised the orbital ephemeris and physical properties of the transiting planet and host star in the WASP-23b system, constructed a broad-band transmission spectrum of WASP-23b and performed a comparative analysis with theoretical models of hot Jupiters. We observed a complete transit of WASP-23b in seven bands simultaneously, using the GROND instrument on the MPG/ESO 2.2m telescope at La Silla Observatory and telescope defocussing. The optical data were taken in the Sloan g',r',i' and z' bands. The resulting light curves are of high quality, with a root-mean-square scatter of the residual as low as 330ppm in the z'-band, with a cadence of 90s. Near-infrared data were obtained in the JHK bands. We performed MCMC analysis of our photometry plus existing radial velocity data to refine measurements of the ephemeris and physical properties of the WASP-23. We constructed a broad-band transmission spectrum of WASP-23b and compared it with a theoretical transmission spectrum of a Hot Jupiter. We measured the central transit time with a precision about 8s. From this and earlier observations we obtain an orbital period of P=2.9444300+/-0.0000011d. Our analysis also yielded a larger radius and mass for the planet (Rp=1.067+0.045-0.038 RJup and, Mp=0.917+0.040-0.039MJup). The transmission spectrum is marginally flat, given the limited precision of the measurements for the planet radius and poor spectral resolution of the data.Comment: 8 pages, 5 figures, accepted for publication in Astronomy & Astrophysic

Entire curves avoiding given sets in C^n

Let $F\subset\Bbb C^n$ be a proper closed subset of $\Bbb C^n$ and $A\subset\Bbb C^n\setminus F$ at most countable ($n\geq 2$). We give conditions of $F$ and $A$, under which there exists a holomorphic immersion (or a proper holomorphic embedding) $\phi:\Bbb C\to\Bbb C^n$ with $A\subset\phi(\Bbb C)\subset\Bbb C^n\setminus F$.Comment: 10 page