Manifolds with cusps. (English) Zbl 0674.57028
Summary: In this paper manifolds with cusps are defined and their properties investigated. Manifolds with cusps are manifolds with boundary where the dimension of the tangent cone at points varies widely with that point. Examples are exponential sums, splines, and polynomials with only real roots. The investigations are motivated by numerical algorithms in approximation theory and other areas.
MSC:
| 57R99 | Differential topology |
| 65D07 | Numerical computation using splines |
| 57Q99 | PL-topology |
| 65D05 | Numerical interpolation |
| 41A15 | Spline approximation |
| 41A99 | Approximations and expansions |
Keywords:
manifolds with cusps; tangent cone; exponential sums; splines; polynomials with only real roots; numerical algorithms in approximation theoryReferences:
| [1] | Cromme, J. Approx. Th. 351 pp 30– (1982) |
| [2] | Approximation auf Mannigfaltigkeiten mit Spitzen-Theorie und numerische Methoden Habilitationsschrift, Göttingen 1979 |
| [3] | Decomposition of Manifolds. Academic Press, London 1986 |
| [4] | Introduction to Global Analysis. Academic Press New York 1980 · Zbl 0443.58001 |
| [5] | Spallek, Math. Ann. 180 pp 269– (1969) |
| [6] | Lectures on Differential Geometry, Prentice Hall, Englewood 1964 · Zbl 0129.13102 |
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