Harmonic maps of V-manifolds

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1989

OSTI ID:5634453

Chiang, Yuan-Jen

Harmonic maps between manifolds are described as the critical maps of their associated energy functionals. By using Sampson's method (Sam1), the author constructs a Sobolev's chain on a compact V-manifold and obtain Rellich's Theorem (Theorem 3.1), Sobolev's Theorem (Theorem 3.2), the regularity theorem (Theorem 3.3), the property of the eigenspaces for the Laplacian (Theorem 3.5) and the solvability of Laplacian (Theorem 3.6). Then, with these results, he constructs the Green's functions for the Laplacian on a compact V-manifold M in Proposition 4.1; and obtain an orthonormal basis for L{sup 2}(M) formed by the eigenfunctions of the Laplacian corresponding to the eigenvalues in Proposition 4.2. He also estimates the eigenvalues and eigenfunctions of the Laplacian in Theorem 4.3, which is used to construct the heat kernel on a compact V-manifold in Proposition 5.1. Afterwards, he compares the G-invariant heat kernel functions with the G-invariant fundamental solutions of heat equations in the finite V-charts of a compact V-manifold in Theorem 6.1, and then study two integral operators associated to the heat kernel on a compact V-manifold in {section}7. With all the preceding results established, in Theorem 8.3 he uses successive approximations to prove the existence of the solutions of parabolic equations on V-manifolds. Finally, he uses Theorem 8.3 to show the existence of harmonic maps from compact V-manifolds into compact Riemannian manifolds in Theorem 9.1 which extends Eells-Sampson's results (E-S).

• Research Organization: Johns Hopkins Univ., Baltimore, MD (USA)
• OSTI ID: 5634453
• Country of Publication: United States
• Language: English

Related Subjects

657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENFUNCTIONS
EIGENVALUES
FUNCTIONS
LAPLACIAN
MAPPING
MAPS
MATHEMATICAL MANIFOLDS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
RIEMANN SPACE
SPACE