Modern Geometry-Methods and Applications(Part II. The Geometry and Topology of Manifolds)

By Boris Dubrovin, S. Novikov, A. Fomenko. 2010

213 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

On the global well-posedness of the one-dimensional Schrodinger map flow (2008, background): “For general n, one gets an expression for a solution of (13) given by the chronological exponential e(t, x+1)= A−1(t, x)e(t, x) := lim n→∞ exp ( − 1 n BU (t, x+1) ) exp ( − 1 n BU (t, x + n−1 n ) ) · · · exp ( − 1 n BU (t, x + 1 n ) ) e(t, 0); (86) see for example [Dubrovin et al. 1985].”
Carleman estimates for parabolic equations with nonhomogeneous boundary conditions (2009, unknown): “Since φ( · , x1, · · · , xn−1, 0) = 1 l(x0) , this implies φ( · , x1, · · · , xn−1, 0) ∈ [2, 2], ∀x0 ∈ Gj and I1 ≤ C‖φ 1 4+ 1 κ ( · , x1, · · · , xn−1, 0)g( · , x1, · · · , xn−1)‖2L2(Gj), (2.”
Differential Geometry of Special Mappings (2019, background): “In a monograph Dubrovin, Fomenko, Novikov [42] a geodesic curve is defined as an extremal of the integral”