Ramified Integrals, Singularities and Lacunas
- ISBN-10
- 9401102139
- ISBN-13
- 9789401102131
- Category
- Mathematics
- Pages
- 306
- Language
- English
- Published
- 2012-12-06
- Publisher
- Springer Science & Business Media
- Author
- V.A. Vassiliev
Description
Solutions to many problems of these theories are treated. Subjects include the proof of multidimensional analogues of Newton's theorem on the nonintegrability of ovals; extension of the proofs for the theorems of Newton, Ivory, Arnold and Givental on potentials of algebraic surfaces. Also, it is discovered for which d and n the potentials of degree d hyperbolic surfaces in [actual symbol not reproducible] are algebraic outside the surfaces; the equivalence of local regularity (the so-called sharpness), of fundamental solutions of hyperbolic PDEs and the topological Petrovskii-Atiyah-Bott-Garding condition is proved, and the geometrical characterization of domains of sharpness close to simple singularities of wave fronts is considered; a 'stratified' version of the Picard-Lefschetz formula is proved, and an algorithm enumerating topologically distinct Morsifications of real function singularities is given.
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