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Currently displaying 1 – 3 of 3

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About a conjecture of F. W. Gehring on the boundary correspondence by quasi-conformal mappings

Petru Caraman — 1976

Annales Polonici Mathematici

Boundary behaviour of quasiconformal mappings in normed spaces

Petru Caraman — 1985

Annales Polonici Mathematici

New cases of equality between p-module and p-capacity

Petru Caraman — 1991

Annales Polonici Mathematici

Let E₀, E₁ be two subsets of the closure D̅ of a domain D of the Euclidean n-space $ℝ^{n}$ and Γ(E₀,E₁,D) the family of arcs joining E₀ to E₁ in D. We establish new cases of equality $M_{p} Γ (E ₀, E ₁, D) = c a p_{p} (E ₀, E ₁, D)$ , where $M_{p} Γ (E ₀, E ₁, D)$ is the p-module of the arc family Γ(E₀,E₁,D), while $c a p_{p} (E ₀, E ₁, D)$ is the p-capacity of E₀,E₁ relative to D and p > 1. One of these cases is when p = n, E̅₀ ∩ E̅₁ = ∅, $E_{i} = E_{i}^{'} \cup E_{i}^{''} \cup E_{i}^{'''} \cup F_{i}$ , $E_{i}^{'}$ is inaccessible from D by rectifiable arcs, $E_{i}^{''}$ is open relative to D̅ or to the boundary ∂D of D, $E_{i}^{'''}$ is at most countable, $F_{i}$ is closed (i = 0,1) and D...

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