On the Problem of Maximizing the Product of Powers of Conformal Radii Nonoverlapping Domains

Emel'yanov, E. G.

doi:10.1023/b:joth.0000035239.55516.08

Cited by 3 publications

(5 citation statements)

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“…We have already commented in the introduction that this relation is proven rigorously in geometric function theory, see [32][33][34][35][36][37][44][45][46][47]. Here we argued in the spirit of Liouville theory which forms a bridge between these previously unrelated sub-fields.…”

Section: Jhep05(2023)186mentioning

confidence: 81%

“…Evaluating S * 0,n (ξ i ; α i ) has a rich and fruitful history in geometric function theory and it goes under the name of the extremal decomposition of Riemann sphere, see [32][33][34][35][36][37][44][45][46][47]. Actually, S * 0,4 (ξ i ) is claimed to have a closed-form expression in term of Jacobi elliptic functions [45,46], and the partial results are known for n ≥ 5, although these expressions seem to be implicit at best.…”

Section: Jhep05(2023)186mentioning

confidence: 99%

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Bootstrapping closed string field theory

Fırat

2023

J. High Energ. Phys.

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The determination of the string vertices of closed string field theory is shown to be a conformal field theory problem solvable by combining insights from Liouville theory, hyperbolic geometry, and conformal bootstrap. We first demonstrate how Strebel differentials arise from hyperbolic string vertices by performing a WKB approximation to the associated Fuchsian equation, which we subsequently use it to derive a Polyakov-like conjecture for Strebel differentials. This result implies that the string vertices are generated by the interactions of n zero momentum tachyons, or equivalently, a certain limit of suitably regularized on-shell Liouville action. We argue that the latter can be related to the interaction of three zero momentum tachyons on a generalized cubic vertex through classical conformal blocks. We test this claim for the quartic vertex and discuss its generalization to higher-string interactions.

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Section: Jhep05(2023)186mentioning

confidence: 81%

Section: Jhep05(2023)186mentioning

confidence: 99%

Bootstrapping closed string field theory

Fırat

2023

J. High Energ. Phys.

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“…Emel'yanov, A. Vasiliev, Ch. Pommerenke used a different approach to study extremal decomposition problems, namely, their technique was based on the method of extremal metric (see for example [7,8,9,10,11] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Extremal decomposition problems for p-harmonic radius

Kalmykov

Prilepkina

2017

Anal Math

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We extend classical results by Lavrent'ev and Kufarev concerning the product of the conformal radii of planar non-overlapping domains. We also extend relatively recent results for the case of domains in the ndimensional Euclidean space, n ≥ 3, with conformal radii replaced by harmonic ones. Namely, we get analogues of these results in n-dimensional Euclidean space in terms of p-harmonic radius. The proofs are based on technique of modulii of curve families and dissymmetrization of such families.

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“…This problem belongs to the class of extremal problems with free poles. Problems of this type have been studied in many papers (see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]). For γ = 1 2 and n 2, an estimate of the functional J n (γ) for the system of non-overlapping domains was found in the paper [6, p. 59].…”

mentioning

confidence: 99%

“…k , ∞} (k = 1, n). An estimate of the functional (7) in the case of fixed poles was first obtained in [6], and then in the papers [9,15]. On the basis of Lemma 4.1.2 [1], we get the estimate…”

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confidence: 99%

Sharp estimates of products of inner radii of non-overlapping domains in the complex plane

Bakhtin¹,

Denega²

2019

Issues of Analysis

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In the paper we study a generalization of the extremal problem of geometric theory of functions of a complex variable on non-overlapping domains with free poles: Fix any γ ∈ R + and find the maximum (and describe all extremals) of the functional [r (B 0 , 0) r (B ∞ , ∞)] γ n k=1 r (B k , a k) , where n ∈ N, n 2, a 0 = 0, |a k | = 1, B 0 , B ∞ , {B k } n k=1 is a system of mutually non-overlapping domains, a k ∈ B k ⊂ C, k = 0, n, ∞ ∈ B ∞ ⊂ C, (r(B, a) is an inner radius of the domain B ⊂ C at a ∈ B). Instead of the classical condition that the poles are on the unit circle, we require that the system of free poles is an n-radial system of points normalized by some "control" functional. A partial solution of this problem is obtained.

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On the Problem of Maximizing the Product of Powers of Conformal Radii Nonoverlapping Domains

Cited by 3 publications

References 1 publication

Bootstrapping closed string field theory

Bootstrapping closed string field theory

Extremal decomposition problems for p-harmonic radius

Sharp estimates of products of inner radii of non-overlapping domains in the complex plane

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