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Differential equations on Riemannian manifolds and their geometric applications. (English) Zbl 0312.53031

MSC:
53C20 Global Riemannian geometry, including pinching
31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
31A35 Connections of harmonic functions with differential equations in two dimensions
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
31B35 Connections of harmonic functions with differential equations in higher dimensions
31C05 Harmonic, subharmonic, superharmonic functions on other spaces
35P15 Estimates of eigenvalues in context of PDEs
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov)
58J40 Pseudodifferential and Fourier integral operators on manifolds
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References:
[1] Theory of Minimal Surfaces and a Counter-Example to the Bernstein Conjecture in High Dimension, Lectures at the Courant Institute, New York University, 1970.
[2] Calabi, Duke Math. J. 25 pp 45– (1958)
[3] Keller, Comm. Pure Appl. Math. 10 pp 503– (1957)
[4] Klotz, Comment. Math. Helv. 41 pp 313– (1966)
[5] Milnor, J. Diff. Geom. 2 pp 1– (1968)
[6] Osserman, Pacific J. Math. 7 pp 1641– (1957) · Zbl 0083.09402 · doi:10.2140/pjm.1957.7.1641
[7] Redheffer, J. Math. Anal. Appl. 1 pp 277– (1960)
[8] Complete Hypersurfaces with Constant Scalar Curvature, Lecture Notes, A.M.S. Symposium, Stanford 1973.
[9] Harmonic functions on Riemannian manifolds, to appear. · Zbl 0267.31008
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