کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4667716 1345475 2007 29 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Holomorphic extensions of Laplacians and their determinants
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Holomorphic extensions of Laplacians and their determinants
چکیده انگلیسی

The Teichmüller space Teich(S) of a surface S in genus g>1 is a totally real submanifold of the quasifuchsian space QF(S). We show that the determinant of the Laplacian det′(Δ) on Teich(S) has a unique holomorphic extension to QF(S). To realize this holomorphic extension as the determinant of differential operators on S, we introduce a holomorphic family {Δμ,ν} of elliptic second order differential operators on S whose parameter space is the space of pairs of Beltrami differentials on S and which naturally extends the Laplace operators of hyperbolic metrics on S. We study the determinant of this family {Δμ,ν} and show how this family realizes the holomorphic extension of det′(Δ) as its determinant.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 211, Issue 2, 1 June 2007, Pages 517-545