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Title of Journal: manuscripta math

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Abbravation: Manuscripta Mathematica

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Springer-Verlag

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10.1002/zfch.19880280818

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1432-1785

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Cut loci and conjugate loci on Liouville surfaces

Authors: Jinichi Itoh Kazuyoshi Kiyohara
Publish Date: 2011/02/10
Volume: 136, Issue: 1-2, Pages: 115-141
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Abstract

In the earlier paper Itoh and Kiyohara Manuscr Math 114247–264 2004 we showed that the cut locus of a general point on twodimensional ellipsoid is a segment of a curvature line and proved “Jacobi’s last geometric statement” on the singularities of the conjugate locus In the present paper we show that a wider class of Liouville surfaces possess such simple cut loci and conjugate loci The results include the determination of cut loci and the set of poles on twosheeted hyperboloids and elliptic paraboloids

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Other Papers In This Journal:
  1. A stability criterion for nonparametric minimal submanifolds
  2. Harmonic maps and asymptotic Teichmüller space
  3. On the backward uniqueness property for the heat equation in two-dimensional conical domains
  4. Minoration de la hauteur de Néron-Tate sur les surfaces abéliennes
  5. Stability of flows associated to gradient vector fields and convergence of iterated transport maps
  6. Willmore submanifolds of the Möbius space and a Bernstein-type theorem
  7. A positivity property of the Satake isomorphism
  8. Homological characterization of lean algebras
  9. Reduction of structure for torsors over semilocal rings
  10. Common divisors of elliptic divisibility sequences over function fields
  11. Finitistic dimensions of semiprimary rings
  12. Extending Elliptic Curve Chabauty to higher genus curves
  13. The Sp 3 -grassmannian and duality for prime Fano threefolds of genus 9
  14. Existence and compactness for the $${\overline{\partial}}$$ -Neumann operator on q-convex domains
  15. The normalization constant of a certain invariant measure on GL n ()
  16. Tropical descendant Gromov–Witten invariants
  17. A Harnack inequality for the quasi-minima of scalar integral functionals with general growth conditions
  18. A sphere theorem on locally conformally flat even-dimensional manifolds
  19. On the class numbers of certain Hilbert class fields
  20. The zeros of certain weakly holomorphic Drinfeld modular forms
  21. Icosahedral representations and elliptic curves
  22. On entire functions whose derivatives are¶integer-valued on geometric progressions
  23. Perversité et variation
  24. On linear combinations of special values of L -functions
  25. Irrationalité de certaines sommes de séries
  26. Deformations of Koszul Artin–Schelter Gorenstein algebras
  27. On positive definite hermitian forms
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