1 - 7 of 7 articles
We consider ergodic optimization for the shift map on the modified Bernoulli space σ: [0, 1]ℕ → [0, 1]ℕ, where [0, 1] is the unit closed interval, and the potential A: [0, 1]ℕ → ℝ considered depends on the two first coordinates of [0, 1]ℕ. We are interested in finding stationary Markov...
It is known that not every Cantor set of S
1 is C
1-minimal. In this work we prove that every member of a subfamily of what we here call regular interval Cantor set is not C
1-minimal. We also prove that no member of a class of Cantor sets that includes this subfamily is C
1+∈-minimal, for any ∈...
be an n-dimensional Euclidean space with n ≥ 2. In this paper, we generalize a classical theorem of Beckman and Quarles by proving that if a mapping, from an open convex subset Co of E
, preserves a distance ρ, then the restriction of f to an open convex subset C
∞ of C
We classify all surfaces in ℍ2 × ℝ for which the unit normal makes a constant angle with the ℝ-direction. Here ℍ2 is the hyperbolic plane.
In this paper, we prove following: If G ⊂ PU (2, 1) is an infinite, discrete group, acting on P
without complex invariant lines, then the component containing ℍP
of the domain of discontinuity Ω(G) = PP
∖ Λ (G), according to Kulkarni, is G-invariant complete Kobayashi hyperbolic.
In this paper the Théodoresco transform is used to show that, under additional assumptions, each Hölder continuous function f defined on the boundary Γ of a fractal domain Ω ⊂ ℝ2n
can be expressed as f = Ψ+ − Ψ−, where Ψ± are Hölder continuous functions on Γ and Hermitian monogenically...
In this paper we study minimal surfaces in M × ℝ, where M is a complete surface. Our main result is a Jenkins-Serrin type theorem which establishes necessary and sufficient conditions for the existence of certain minimal vertical graphs in M × ℝ. We also prove that there exists a unique solution...
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