## Seminar on Nonlinear Partial Differential Equations |

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### Contents

Geometrical and Analytical Questions Stuart S Antman | 1 |

An Introduction to Eulers Equations Alexandre J Chorin | 31 |

The Ricci Curvature Equation Richard Hamilton | 47 |

Copyright | |

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### Common terms and phrases

analytic functions Antman argument assume ball Bernstein\s Theorem bounded codimension coefficients compact support constant convergence convex function coordinate critical points curve defined deformation denote density derivatives differential inequality differential operator dimension Dirichlet distribution solutions domain DRc(g elliptic elliptic operators energy entire solution entropy estimates existence finite flow fluid follows formula geometry given gradient Hamiltonian harmonic map hence hypersurfaces implies inequality initial data integral Lemma linear manifolds Marsden Math mathematical maximum principle mechanics membrane metric g minimal surface minimal surface equation Navier-Stokes equations neighborhood nonlinear elasticity nonpositive norm partial differential equations plane plasma Poisson Poisson bracket positive proof prove Rc(g removable singularities Ricci curvature Riemannian satisfies shock smooth space strictly hyperbolic submanifold subset Suppose tensor theory ulel unique variables variation velocity viscosity vortex vorticity weak solution weakly harmonic