240b Class Note
نویسنده
چکیده
1. Integration on manifolds. 1 2. The extension of the Levi-Civita connection. 4 3. Covariant derivatives. 7 4. The Laplace operator. 9 5. Self-adjoint extension of the Laplace operator. 11 6. The Poincaré Lemma. 13 7. de Rham Theorem. 14 8. Formal Hodge Theorem. 16 9. The Hodge theorem. 17 10. Proof of the Hodge Theorem. 17 11. More about elliptic regularity. 22 12. Semigroups and their generators. 24 13. Heat kernel. 26 14. Variational characterization of spectrum. 30 15. Poincaré inequality and Sobolev inequality. 36 16. De Giorgi-Nash-Moser Estimates. 38 17. Aleksandrov maximum principle. 43 18. Krylov-Safonov Estimates. 49
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The Effect ofAbbreviation as a Note- taking Aid On The Reproduction/Reconstruction of Class Lectures
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