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151.
This paper proves a strong convergence theorem for sequences of pseudo-holomorphic maps from a Riemann surface to a symplectic
manifoldN with tamed almost complex structure. (These are the objects used by Gromov to define his symplectic invariants.) The paper
begins by developing some analytic facts about such maps, including a simple new isoperimetric inequality and a new removable
singularity theorem.
The main technique is a general procedure for renormalizing sequences of maps to obtain “bubbles on bubbles.” This is a significant
step beyond the standard renormalization procedure of Sacks and Uhlenbeck. The renormalized maps give rise to a sequence of
maps from a “bubble tree”—a map from a wedge Σ V S2 V S2 V ... →N. The main result is that the images of these renormalized maps converge in L1,2 ∪C° to the image of a limiting pseudo-holomorphic map from the bubble tree. This implies several important properties of the
bubble tree. In particular, the images of consecutive bubbles in the bubble tree intersect, and if a sequence of maps represents
a homology class then the limiting map represents this class. 相似文献
152.
Thehomotopical rank of a mapf:M →N is, by definition, min{dimg(M) ¦g homotopic tof}. We give upper bounds for this invariant whenM is compact Kähler andN is a compact discrete quotient of a classical symmetric space, e.g., the space of positive definite matrices. In many cases the upper bound is sharp and is attained by geodesic immersions of locally hermitian symmetric spaces. An example is constructed (Section 9) to show that there do, in addition, exist harmonic maps of quite a different character. A byproduct is construction of an algebraic surface with large and interesting fundamental group. Finally, a criterion for lifting harmonic maps to holomorphic ones is given, as is a factorization theorem for representations of the fundamental group of a compact Kähler manifold. The technique for the main result is a combination of harmonic map theory, algebra, and combinatorics; it follows the path pioneered by Siu in his ridigity theorem and later extended by Sampson. 相似文献
153.
Peter Scharfenberg 《Theoretical chemistry accounts》1980,58(1):73-79
A simple classification scheme is proposed for critical points, based only on rankr and signatures of the (n,n)-matrixG of harmonic force constants. The determination ofr ands, e.g. by the well-known factorizationG=L
T
gL (L: triangular matrix,g: diagonal matrix), has several theoretical as well as practical (computational) advantages over the inspection of eigenvalues ofG, so far used in quantum chemistry. The eigenvalues are sufficient butnot necessary for a classification whereas rank and signature are the only necessary and sufficient prerequisites for solving the task. For the purpose of presenting a working example, by calculating only a 2×2 torque constant matrix, it is shown that the coplanar ethylbenzene is unstable in the CNDO/2 picture. 相似文献
154.
In this paper we investigate a class of Lie group actions on
, the so-calledpolar actions, that naturally generalize the standard
actions. For a domain invariant under such an action (i.e., a generalized Reinhardt domain) we characterize the invariant
plurisubharmonic functions and determine the envelope of holomorphy in geometric terms. For a generalized Reinhardt domain
containing the origin of
we also compute its automorphism group.
Supported in part by NSF Grant 8602020 相似文献
155.
It has been conjectured that a lattice in a noncompact group of real rank one, other than SU(1,n), cannot be isomorphic to the fundamental group of a compact Kähler manifold; moreover, it is known to be true for SO(1,n). In this note it is shown that this conjecture also holds for the case of uniform lattices in F4(?20), the group of isometries of the Cayley hyperbolic plane. The result is a consequence of a classification theorem for harmonic maps between Kähler and Cayley hyperbolic manifolds. 相似文献
156.
Roy Mathias 《Numerische Mathematik》1992,63(1):213-226
LetM
n
denote the space ofn×n matrices. GivenX, ZM
n
define
相似文献
157.
Suppose Ω is a smooth domain in Rm,N is a compact smooth Riemannian manifold, andZ is a fixed compact subset of Ω having finite (m − 3)-dimensional Minkowski content (e.g.,Z ism − 3 rectifiable). We consider various spaces of harmonic mapsu: Ω →N that have a singular setZ and controlled behavior nearZ. We study the structure of such spacesH and questions of existence, uniqueness, stability, and minimality under perturbation. In caseZ = 0,H is a Banach manifold locally diffeomorphic to a submanifold of the product of the boundary data space with a finite-dimensional
space of Jacobi fields with controlled singular behavior. In this smooth case, the projection ofu εH tou |ϖΩ is Fredholm of index 0.
R. H.’s research partially supported by the National Science Foundation. 相似文献
158.
We study topological conditions that must be satisfied by a compactC ∞ Levi-flat hypersurface in a two-dimensional complex manifold, as well as related questions about the holonomy of Levi-flat hypersurfaces. As a consequence of our work, we show that no two-dimensional complex manifold admits a subdomain Ω with compact nonemptyC ∞ boundary such that Ω ? ?2. 相似文献
159.
Chi-Keung Cheung 《Journal of Geometric Analysis》1992,2(2):105-119
In this paper we considered curvature conditions on a Kähler-Einstein surface of general type. In particular we showed that it has negative holomorphic sectional curvature if theL 2-norm of (3C 2 ?C 1 2 )/C 1 2 is sufficiently small, whereC 1 andC 2 are the first and second Chern classes of the surfaces. This generalizes a result of Yau on the uniformization of Kähler-Einstein surfaces of general type and with 3C 2 ?C 1 2 = 0. Also in the process, we obtain a necessary condition in terms of an inequality between Chern numbers for a Kähler-Einstein metric to have negative holomorphic sectional curvature. 相似文献
160.
We add to the known examples of complete Kähler manifolds with negative sectional curvature by showing that the following three classes of domains in euclidean spaces also belong: perturbations of ellipsoidal domains in ?n, intersections of complex-ellipsoidal domains in ?2, and intersections of fractional linear transforms of the unit ball in ?2. In the process, we prove the following theorem in differential geometry: in the intersection of two complex-ellipsoidal domains in ?2, the sum of the Bergman metrics is a Kähler metric with negative curvature operator. 相似文献
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