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This is a write-up on the foundation of the Sobolev Institute of Mathematics in 1957. 相似文献
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We study the generalization of the Willmore functional for surfaces in the three-dimensional Heisenberg group. Its construction is based on the spectral theory of the Dirac operator entering into theWeierstrass representation of surfaces in this group. Using the surfaces of revolution we demonstrate that the generalization resembles the Willmore functional for the surfaces in the Euclidean space in many geometrical aspects. We also observe the relation of these functionals to the isoperimetric problem. 相似文献
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I. A. Taimanov 《Acta Appl Math》1994,36(1-2):119-124
The-parametrized family of two-gap elliptic potentials is constructed so that (i) 0<<1, (ii) for rational values of such potentials are elliptic (i.e., double-periodic), (iii) within the limit0 this family degenerates to the soliton potential, (iv) within the limit1 this family degenerates to the one-gap Lamé potential.Dedicated to the memory of J.-L. Verdier 相似文献
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We show that one can define a spectral curve for the Cauchy-Riemann operator on a punctured elliptic curve under appropriate boundary conditions. The algebraic curves thus obtained arise, for example, as irreducible components of the spectral curves of minimal tori with planar ends in ?3. It turns out that these curves coincide with the spectral curves of certain elliptic KP solitons studied by Krichever. 相似文献
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Using analytic methods of finite-gap integration, we construct quasihomogeneous algebraic solutions of the WDVV associativity
equations and the nonsemisimple Frobenius manifolds associated with them.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 2, pp. 195–206, May, 2007. 相似文献
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R. G. Novikov I. A. Taimanov 《Proceedings of the Steklov Institute of Mathematics》2018,302(1):315-324
Formulas relating Poincaré–Steklov operators for Schrödinger equations related by Darboux–Moutard transformations are derived. They can be used for testing algorithms of reconstruction of the potential from measurements at the boundary. 相似文献