Metrics of constant positive curvature with four conic singularities on the sphere

Erëmenko, Alexandre

doi:10.1090/proc/15012

Cited by 24 publications

(22 citation statements)

References 45 publications

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“…α a δ 2 (z − z a ), (1.2) where N denotes the number of branes, localized at positions z a and tensions α a . This can be solved analytically up to N = 3 [20,21,22,23]. By use of such results, we demonstrate that forms of KK zero mode wavefunctions are strongly peaked in the vicinity of the brane positions, argued in Ref.…”

Section: Introductionsupporting

confidence: 53%

Wavefunctions on S2 with flux and branes

Imai

Tatsuta

2019

J. High Energ. Phys.

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We formulate a six dimensional U (1) gauge theory compactified on a (two dimensional) sphere S 2 with flux and localized brane sources. Profiles of the lowest Kaluza-Klein (KK) wavefunctions and their masses are derived analytically. In contrast to ordinary sphere compactifications, the above setup can lead to the degeneracy of and the sharp localizations of the linearly independent lowest KK modes, depending on the number of branes and their tensions. Moreover, it can naturally accommodate CP violation in Yukawa interactions. *

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Section: Introductionsupporting

confidence: 53%

Wavefunctions on S2 with flux and branes

Imai

Tatsuta

2019

J. High Energ. Phys.

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“…When k = 2, Troyanov [22] gave the results. When k = 3, the characterization via complex analytical methods was given by Eremenko [8] and Umehara-Yamada [23]. When k = 4 with symmetry, complex analysis techniques can also be applied, see Eremenko-Gabrielov-Tarasov [10].…”

Section: Review Of Existing Resultsmentioning

confidence: 99%

Conical metrics on Riemann surfaces, I: The compactified configuration space and regularity

Mazzeo

Zhu

2020

Geom. Topol.

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We introduce a compactification of the space of simple positive divisors on a Riemann surface, as well as a compactification of the universal family of punctured surfaces above this space. These are real manifolds with corners. We then study the space of constant curvature metrics on this Riemann surface with prescribed conical singularities at these divisors. Our interest here is in the local deformation for these metrics, and in particular the behavior as conic points coalesce. We prove a sharp regularity theorem for this phenomenon in the regime where these metrics are known to exist. This setting will be used in a subsequent paper to study the space of spherical conic metrics with large cone angles, where the existence theory is still incomplete.

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“…For example, Nitsch [Nit57], Heins [Hei62] and Yamada [Yam88] proved that an isolated singularity of a hyperbolic metric is either a conical singularity or a cusp one, and Heins [Hei62], Mcowen [McO88] and Troyanov [Tro91] independently gave a necessary and sufficient condition for the existence of a unique hyperbolic metric, which has the prescribed conical or cusp singularities, on a compact Riemann surface. Among all the research on singular metrics on Riemann surfaces, developing maps, due to [Bry87,UY00,Ere04], prove to be a very useful tool. By considering the monodromy of developing maps in [CWWX15], Chen and coauthors constructed a new class of cone spherical metrics.…”

Section: Introductionmentioning

confidence: 99%