Behavior of invariant metrics near convexifiable boundary points

Nikolai Nikolov

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Local uniform linear convexity with respect to the Kobayashi distance.

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Trivial generators for nontrivial fibres

Linus Carlsson (2008)

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Pseudoconvex domains are exhausted in such a way that we keep a part of the boundary fixed in all the domains of the exhaustion. This is used to solve a problem concerning whether the generators for the ideal of either the holomorphic functions continuous up to the boundary or the bounded holomorphic functions, vanishing at a point in $ℂ^{n}$ where the fibre is nontrivial, has to exceed $n$ . This is shown not to be the case.

Reinhardt domains and the Gleason problem

Oscar Lemmers, Jan Wiegerinck (2001)

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Nonuniqueness for some linear oblique derivative problems for elliptic equations

Gary M. Lieberman (1999)

Commentationes Mathematicae Universitatis Carolinae

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It is well-known that the “standard” oblique derivative problem, $Δ u = 0$ in $Ω$ , $\partial u / \partial ν - u = 0$ on $\partial Ω$ ( $ν$ is the unit inner normal) has a unique solution even when the boundary condition is not assumed to hold on the entire boundary. When the boundary condition is modified to satisfy an obliqueness condition, the behavior at a single boundary point can change the uniqueness result. We give two simple examples to demonstrate what can happen.

Behavior of the Carathéodory metric near strictly convex boundary points.

Jarnicki, Marek, Nikolov, Nikolai (2002)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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