Geodesic
The Heat Equation for the -Neumann Problem, II
Canadian journal of mathematics, Tome 40 (1988) no. 2, pp. 502-512

Voir la notice de l'article provenant de la source Cambridge University Press

Let Ω be a compact complex n + 1-dimensional Hermitian manifold with smooth boundary M. In [2] we proved the following.THEOREM 1. Suppose satisfies condition Z(q) with 0 ≦ q ≦ n. Let □p,q denote the -Laplacian on (p, q) forms onwhich satisfy the -Neumann boundary conditions. Then as t → 0;, (0.1) (If q = n + 1, the -Neumann boundary condition is the Dirichlet boundary condition and the corresponding result is classical.)Theorem 1 is a version for the -Neumann problem of results initiated by Minakshisundaram and Pleijel [8] for the Laplacian on compact manifolds and extended by McKean and Singer [7] to the Laplacian with Dirichlet or Neumann boundary conditions and by Greiner [5] and Seeley [9] to elliptic boundary value problems on compact manifolds with boundary. McKean and Singer go on to show that the coefficients in the trace expansion are integrals of local geometric invariants. 
Beals, Richard; Stanton, Nancy K. The Heat Equation for the -Neumann Problem, II. Canadian journal of mathematics, Tome 40 (1988) no. 2, pp. 502-512. doi: 10.4153/CJM-1988-021-8
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