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This book deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber bundles, ideas concerning points of concentration, blowing-up technique, geometric and topological methods. It explores important geometric problems that are of interest to many mathematicians and scientists but have only recently been partially solved.

Some Nonlinear Problems in Riemannian Geometry

1 Riemannian Geometry.- 2 Sobolev Spaces.- 3 Background Material.- 4 Complementary Material.- 5 The Yamabe Problem.- 6 Prescribed Scalar Curvature.- 7 Einstein-Kähler Metrics.- 8 Monge-Ampere Equations.- 9 The Ricci Curvature.- 10 Harmonic Maps.- Bibliography*.- Notation.