Spherical conical metrics and harmonic maps to spheres
نویسندگان
چکیده
A spherical conical metric g g on a surface alttext="normal upper Sigma"> Σ encoding="application/x-tex">\Sigma is of constant curvature alttext="1"> 1 encoding="application/x-tex">1 with finitely many isolated singularities. The uniformization problem for such metrics remains largely open when at least one the cone angles exceeds alttext="2 pi"> 2 π<!-- π </mml:mrow> encoding="application/x-tex">2\pi . eigenfunctions Friedrichs Laplacian Delta Subscript g"> mathvariant="normal">Δ<!-- Δ </mml:msub> encoding="application/x-tex">\Delta _g eigenvalue alttext="lamda equals 2"> λ<!-- λ <mml:mo>= encoding="application/x-tex">\lambda =2 play special role in this problem, as they represent local obstructions to deformations class metrics. In present paper we apply theory multivalued harmonic maps spheres question existence eigenfunctions. first part establish new criterion alttext="2"> encoding="application/x-tex">2 -eigenfunctions, given terms certain meromorphic data As an application give description all -eigenfunctions sphere most three second algebraic construction large number via deformation maps. We provide explicit examples both approaches, and describe general algorithm find arbitrarily -eigenfunctions.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2022
ISSN: ['2330-0000']
DOI: https://doi.org/10.1090/tran/8578