Hyperelliptic action integral

Elsner, Bernhard

doi:10.5802/aif.1675

Cited by 6 publications

(6 citation statements)

References 8 publications

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“…Finally in the proof of Theorem A, the local type of analysis needed to conclude, for example, the bounded nature of the projective structure in question will take us close to an interesting conjecture put forward by B. Elsner in [6], cf. Proposition 4.2.…”

Section: Introductionmentioning

confidence: 73%

“…As an exemple, we state Proposition 5.7 (see Remark 5.6) that also appears in problems about vector fields having univalued solutions, see for example [13] and its references. Also, let us point out that Proposition 4.2 is a special case of a nice conjecture put forward in [6]: it might be interesting to check how far our method can be pushed to provide insight in Elsner's conjecture.…”

Section: Proof Of Proposition 42mentioning

confidence: 99%

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Uniformizable singular projective structures on Riemann surface orbifolds

Elshafei¹,

Rebelo²,

Reis³

2022

Preprint

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This paper is devoted to characterizing complex projective structures defined on Riemann surface orbifolds and giving rise to injective developing maps defined on the monodromy covering of the surface (orbifold) in question. The relevance of these structures stems from several problems involving vector fields with uniform solutions as well as from problems about "simultaneous uniformization" for leaves of foliations by Riemann surfaces. In this paper, we first describe the local structure of the mentioned projective structures showing, in particular, that they are locally bounded. In the case of Riemann surface orbifolds of finite type, the previous result will then allow us to provide a detailed global picture of these projective structures by exploiting their connection with the class of "bounded covering projective structures".

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Section: Introductionmentioning

confidence: 73%

Section: Proof Of Proposition 42mentioning

confidence: 99%

Uniformizable singular projective structures on Riemann surface orbifolds

Elshafei¹,

Rebelo²,

Reis³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…To avoid nonphysical singularity, we restrict our discussions for m ≤ 2 and hence we only consider the q ≥ Ϫ 10 ϩ 4͙6 branch (for a discussion about the essential singularity at infinity, we refer the reader to ref. 42). Now, we discuss some specific values of allowed q.…”

Section: Appendix Amentioning

confidence: 93%

Asymptotically Lifshitz black hole solutions in F(R) gravity

2014

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We consider a class of spherically symmetric spacetime to obtain some interesting solutions in F(R) gravity without matter field (pure gravity). We investigate the geometry of the solutions and find that there is an essential singularity at the origin. In addition, we show that there is an analogy between obtained solutions with the black holes of Einstein-Lambda -power-Maxwell-invariant theory. Furthermore, we find that these solutions are equivalent to the asymptotically Lifshitz black holes. Also, we calculate d^2F/dR^2 to examine the Dolgov-Kawasaki stability criterion.Comment: Accepted for publication in Canadian Journal of Physic

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“…Concerning F (z), one has the following property. When V (q) is an entire function (or even a meromorphic one), a more precise result can be obtained, using the well-known properties of the transformation q → q V (t) 1 2 dt in terms of conformal mapping, e.g., [16,19,29]. Fig.…”

Section: Applications For the Schrödinger Equationmentioning

confidence: 99%

Quantum resurgence for a class of Airy type differential equations

Rasoamanana

2008

Journal of Differential Equations

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In this article, we investigate the resurgent properties of divergent WKB solutions of a class of Airy type perturbed differential equations. In particular, we extend and propose a new proof of a reduction theorem, due to Aoki et al. [T. Aoki, T. Kawai, Y. Takei, The Bender-Wu analysis and the Voros theory, in: Special Functions, ICM-90 Satell. Conf. Proc., Okayama, 1990, Springer, Tokyo, 1991, near a simple turning point, in the framework of exact WKB analysis. Our scheme of proof is based on a Laplace-integral representation derived from an existence theorem of holomorphic solutions for a singular linear partial differential equation.

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Hyperelliptic action integral

Cited by 6 publications

References 8 publications

Uniformizable singular projective structures on Riemann surface orbifolds

Uniformizable singular projective structures on Riemann surface orbifolds

Asymptotically Lifshitz black hole solutions in F(R) gravity

Quantum resurgence for a class of Airy type differential equations

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