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101.
Misha Verbitsky 《Selecta Mathematica, New Series》2005,10(4):551-559
For any subvariety of a compact holomorphic symplectic K?hler manifold, we define the symplectic Wirtinger number W(X). We show that
W(X) \leqslant 1,W(X) \leqslant 1, and the equality is reached if and only if the subvariety
X ì MX \subset M is trianalytic, i.e. compatible with the hyperk?hler structure on M. For a sequence
X1 ? X2 ? ?Xn ? MX_1 \to X_2 \to \ldots X_n \to M of immersions of simple holomorphic symplectic manifolds, we show that
W( X1 ) \leqslant W( X2 ) \leqslant ?\leqslant W( Xn ).W\left( {X_1 } \right) \leqslant W\left( {X_2 } \right) \leqslant \ldots \leqslant W\left( {X_n } \right). 相似文献
102.
In order to quantitatively illustrate the rôle of positivity in the Falconer distance problem, we construct a family of sign indefinite, compactly supported measures in \({\Bbb R}^d\), such that their Fourier transform and Fourier energy of dimension \(s \in (0, d)\) are uniformly bounded. However, the Mattila integral, associated with the Falconer distance problem for these measures is unbounded in the range \(0 < s < \frac{d^2}{2d-1}\). 相似文献
103.
Summary A typical property of greases, as plastic disperse systems, is their thixotropy (reversible destruction of their structure due to deformation). In relation to this, if the rate of their formation drops below a certain critical value it becomes practically very difficult or even impossible to attain steady conditions of their flow. This is observed both in rotational plastoviscometers and in rolling-contact bearings, and is manifested in more or less sharp fluctuations of the resistance moments. The critical value of the rate of deformation depends on the nature of the grease and the rigidity of the braking device or the power reserve of the drive, decreasing when these values are increased. When soap greases are deformed they become anisotropic, which, when the direction of deformation is changed, tells perceptibly on their resistance to deformation and results in fluctuations of the resistance moments in rolling bearings. 相似文献
104.
Misha Vishik 《Communications in Mathematical Physics》2000,213(3):697-731
In this paper we study solutions to the Euler equations of an ideal incompressible fluid in R
n
singular at the origin with a finite symmetry group. For an “admissible” class of finite groups we prove a local existence
and uniqueness theorem. In even dimensions this theorem covers some symmetric flows with essentially unbounded vorticity.
In arbitrary dimension (including n=3) we construct local in time solutions with vorticity that behaves, e.g., like a function of homogeneous degree zero near
the origin. The symmetry condition provides necessary additional cancellations and is preserved by the evolution due to uniqueness.
Received: 31 March 1999 / Accepted: 10 July 2000 相似文献
105.
Misha Gromov 《Central European Journal of Mathematics》2014,12(7):923-951
We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all ?∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f. We show, for instance, that if X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume. 相似文献
106.
Misha Gromov 《Central European Journal of Mathematics》2014,12(8):1109-1156
Groping our way toward a theory of singular spaces with positive scalar curvatures we look at the Dirac operator and a generalized Plateau problem in Riemannian manifolds with corners. Using these, we prove that the set of C 2-smooth Riemannian metrics g on a smooth manifold X, such that scal g (x) ≥ κ(x), is closed under C 0-limits of Riemannian metrics for all continuous functions κ on X. Apart from that our progress is limited but we formulate many conjectures. All along, we emphasize geometry, rather than topology of manifolds with their scalar curvatures bounded from below. 相似文献
107.
108.
109.
We consider a multidimensional Burgers equation on the torus Td and the whole space Rd. We show that, in case of the torus, there exists a unique global solution in Lebesgue spaces. For a torus we also provide estimates on the large time behaviour of solutions. In the case of Rd we establish the existence of a unique global solution if a Beale-Kato-Majda type condition is satisfied. To prove these results we use the probabilistic arguments which seem to be new. 相似文献
110.
It is proved that any steady 2 dimensional ideal fluid flow is nonlinearly unstable with respect to L
2
growth in the velocity, provided there exists an eigenvalue for the linearised Euler equation with Re>. Here is the maximal Lyapunov exponent of the steady flow. 相似文献