Filling area conjecture and ovalless real hyperelliptic surfaces

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Filling area conjecture and ovalless real hyperelliptic surfaces. / Bangert, V.; Croke, C.; Ivanov, S.; Katz, M.

In: Geometric and Functional Analysis, Vol. 15, No. 3, 01.06.2005, p. 577-597.

Research output: Contribution to journal › Article › peer-review

Author

Bangert, V. ; Croke, C. ; Ivanov, S. ; Katz, M. / Filling area conjecture and ovalless real hyperelliptic surfaces. In: Geometric and Functional Analysis. 2005 ; Vol. 15, No. 3. pp. 577-597.

BibTeX

@article{4383f03e24884ceb9a564b32eb779357,

title = "Filling area conjecture and ovalless real hyperelliptic surfaces",

abstract = "We prove the filling area conjecture in the hyperelliptic case. In particular, we establish the conjecture for all genus 1 fillings of the circle, extending P. Pu's result in genus 0. We translate the problem into a question about closed ovalless real surfaces. The conjecture then results from a combination of two ingredients. On the one hand, we exploit integral geometric comparison with orbifold metrics of constant positive curvature on real surfaces of even positive genus. Here the singular points are Weierstrass points. On the other hand, we exploit an analysis of the combinatorics on unions of closed curves, arising as geodesics of such orbifold metrics.",

author = "V. Bangert and C. Croke and S. Ivanov and M. Katz",

year = "2005",

month = jun,

day = "1",

doi = "10.1007/s00039-005-0517-8",

language = "English",

volume = "15",

pages = "577--597",

journal = "Geometric and Functional Analysis",

issn = "1016-443X",

publisher = "Birkh{\"a}user Verlag AG",

number = "3",

}

RIS

TY - JOUR

T1 - Filling area conjecture and ovalless real hyperelliptic surfaces

AU - Bangert, V.

AU - Croke, C.

AU - Ivanov, S.

AU - Katz, M.

PY - 2005/6/1

Y1 - 2005/6/1

N2 - We prove the filling area conjecture in the hyperelliptic case. In particular, we establish the conjecture for all genus 1 fillings of the circle, extending P. Pu's result in genus 0. We translate the problem into a question about closed ovalless real surfaces. The conjecture then results from a combination of two ingredients. On the one hand, we exploit integral geometric comparison with orbifold metrics of constant positive curvature on real surfaces of even positive genus. Here the singular points are Weierstrass points. On the other hand, we exploit an analysis of the combinatorics on unions of closed curves, arising as geodesics of such orbifold metrics.

AB - We prove the filling area conjecture in the hyperelliptic case. In particular, we establish the conjecture for all genus 1 fillings of the circle, extending P. Pu's result in genus 0. We translate the problem into a question about closed ovalless real surfaces. The conjecture then results from a combination of two ingredients. On the one hand, we exploit integral geometric comparison with orbifold metrics of constant positive curvature on real surfaces of even positive genus. Here the singular points are Weierstrass points. On the other hand, we exploit an analysis of the combinatorics on unions of closed curves, arising as geodesics of such orbifold metrics.

UR - http://www.scopus.com/inward/record.url?scp=24944544831&partnerID=8YFLogxK

U2 - 10.1007/s00039-005-0517-8

DO - 10.1007/s00039-005-0517-8

M3 - Article

AN - SCOPUS:24944544831

VL - 15

SP - 577

EP - 597

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

SN - 1016-443X

IS - 3

ER -

ID: 49985525