The BFK-gluing formula and the curvature tensors on a 2-dimensional compact hypersurface

  • Klaus Kirsten

    Baylor University, Waco, USA
  • Yoonweon Lee

    Inha University, Incheon, Republic of Korea
The BFK-gluing formula and the curvature tensors on a 2-dimensional compact hypersurface cover

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Abstract

In the proof of the BFK-gluing formula for zeta-determinants of Laplacians there appears a real polynomial whose constant term is an important ingredient in the gluing formula. This polynomial is determined by geometric data on an arbitrarily small collar neighborhood of a cutting hypersurface. In this paper we express the coefficients of this polynomial in terms of the scalar and principal curvatures of the cutting hypersurface embedded in the manifold when this hypersurface is 2-dimensional. Similarly, we express some coefficients of the heat trace asymptotics of the Dirichlet-to-Neumann operator in terms of the scalar and principal curvatures of the cutting hypersurface.

Cite this article

Klaus Kirsten, Yoonweon Lee, The BFK-gluing formula and the curvature tensors on a 2-dimensional compact hypersurface. J. Spectr. Theory 10 (2020), no. 3, pp. 1007–1051

DOI 10.4171/JST/320