In this paper, we give weak regularity theorems on P of u~ε(x, P), where u~ε(x, P)is the viscosity solution of the cell problem H_ε(P D_xu~ε, x)=H_ε(P). 相似文献
Let X be a compact complex manifold which is the image of a complex torus by a holomorphic surjective map A→X. We prove that X is Kähler and that up to a finite étale cover, X is a product of projective spaces by a torus. 相似文献
We conjecture that a Willmore torus having Willmore functional between 2π2 and 2π2\(\sqrt 3 \) is either conformally equivalent to the Clifford torus, or conformally equivalent to the Ejiri torus. Ejiri’s torus in S5 is the first example of Willmore surface which is not conformally equivalent to any minimal surface in any real space form. Li and Vrancken classified all Willmore surfaces of tensor product in Sn by reducing them into elastic curves in S3, and the Ejiri torus appeared as a special example. In this paper, we first prove that among all Willmore tori of tensor product, the Willmore functional of the Ejiri torus in S5 attains the minimum 2π2\(\sqrt 3 \), which indicates our conjecture holds true for Willmore surfaces of tensor product. Then we show that all Willmore tori of tensor product are unstable when the co-dimension is big enough. We also show that the Ejiri torus is unstable even in S5. Moreover, similar to Li and Vrancken, we classify all constrained Willmore surfaces of tensor product by reducing them with elastic curves in S3. All constrained Willmore tori obtained this way are also shown to be unstable when the co-dimension is big enough. 相似文献
Suppose that an algebraic torus G acts algebraically on a projective manifold X with generically trivial stabilizers. Then the Zariski closure of the set of pairs {(x,y)∈X×X|y=gx for some g∈G} defines a nonzero equivariant cohomology class . We give an analogue of this construction in the case where X is a compact symplectic manifold endowed with a Hamiltonian action of a torus, whose complexification plays the role of G. We also prove that the Kirwan map sends the class [ΔG] to the class of the diagonal in each symplectic quotient. This allows to define a canonical right inverse of the Kirwan map. 相似文献
In this paper we introduce a new type of folding called equi-Gaussian curvature folding of connected Riemannian 2-manifolds.
We prove that the composition and the cartesian product of such foldings is again an equi-Gaussian curvature folding. In case
of equi-Gaussian curvature foldings, f: M → Pn, of an orientable surface M onto a polygon Pn we prove that
We produce skew loops—loops having no pair of parallel tangent lines—homotopic to any loop in a flat torus or other quotient of Rn. The interesting case here is n = 3. More subtly for any n, we characterize the homotopy classes that will contain a skew loop having a specified loop as tangent indicatrix.
A fellowship from the Lady Davis foundation helped support this work. 相似文献
In 1991, Turaev and Viro constructed a quantum topological linear representation of mapping class groups of closed surfaces.
To the mappings of a surface into itself, they assigned simple polyhedra whose boundaries consisted of two simple graphs cutting
the surface into cells. The computational complexity of the Turaev-Viro representations strongly depends on the choice of
suitable sets of simple polyhedra. In this paper, simple polyhedra for the torus are constructed. One of the reasons why they
are convenient is that they all are obtained by gluing along boundary of copies of the same simple polyhedron.
Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 533–539, October, 1999. 相似文献
Metal‐stabilized belts : A torus, 3 , consisting of three four‐ and three eight‐membered conjugated rings and stabilized by (RCp)Co‐ and (RCp)Rh‐ units, was generated by irradiation of [(RCp)Co(CO)2] and [(RCp)Rh(C2H4)2], respectively, and 1 .
Let M be a closed 5-manifold of pinched curvature 0<δ?secM?1. We prove that M is homeomorphic to a spherical space form if one of the following conditions holds:
(i)
The center of the fundamental group has index ?w(δ), a constant depending on δ;
(ii)
and the fundamental group is a non-cyclic group of order ?C, a constant;
(iii)
The volume is less than ?(δ) and the fundamental group is either isomorphic to a spherical 5-space group or has an odd order, and it has a center of index ?w, a constant.