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The Maslov Index in PDEs Geometry

In: Essays in Mathematics and its Applications

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  • Agostino Prástaro

    (University of Roma La Sapienza)

Abstract

It is proved that the Maslov index naturally arises in the framework of PDEs geometry. The characterization of PDE solutions by means of Maslov index is given. With this respect, Maslov index for Lagrangian submanifolds is given on the ground of PDEs geometry. New formulas to calculate bordism groups of (n − 1)-dimensional compact submanifolds bording via n-dimensional Lagrangian submanifolds of a fixed 2n-dimensional symplectic manifold are obtained too. As a by-product, it is given a new proof of global smooth solutions existence, defined on all $$\mathbb{R}^{3}$$ , for the Navier–Stokes PDE. Further, complementary results are given in Appendices concerning Navier–Stokes PDE and Legendrian submanifolds of contact manifolds.

Suggested Citation

  • Agostino Prástaro, 2016. "The Maslov Index in PDEs Geometry," Springer Books, in: Themistocles M. Rassias & Panos M. Pardalos (ed.), Essays in Mathematics and its Applications, pages 311-359, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-31338-2_13
    DOI: 10.1007/978-3-319-31338-2_13
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