共查询到20条相似文献,搜索用时 93 毫秒
1.
The higher order degrees are Alexander-type invariants of complements to an affine plane curve. In this paper, we characterize the vanishing of such invariants for a curve C given as a transversal union of plane curves and in terms of the finiteness and the vanishing properties of the invariants of and , and whether or not they are irreducible. As a consequence, we prove that the multivariable Alexander polynomial is a power of , and we characterize when in terms of the defining equations of and . Our results impose obstructions on the class of groups that can be realized as fundamental groups of complements of a transversal union of curves. 相似文献
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Let be either a simply connected space form or a rank-one symmetric space of the noncompact type. We consider Weingarten hypersurfaces of , which are those whose principal curvatures and angle function satisfy a relation , being W a differentiable function which is symmetric with respect to . When on the positive cone of , a strictly convex Weingarten hypersurface determined by W is said to be elliptic. We show that, for a certain class of Weingarten functions W, there exist rotational strictly convex Weingarten hypersurfaces of which are either topological spheres or entire graphs over M. We establish a Jellett–Liebmann-type theorem by showing that a compact, connected and elliptic Weingarten hypersurface of either or is a rotational embedded sphere. Other uniqueness results for complete elliptic Weingarten hypersurfaces of these ambient spaces are obtained. We also obtain existence results for constant scalar curvature hypersurfaces of and which are either rotational or invariant by translations (parabolic or hyperbolic). We apply our methods to give new proofs of the main results by Manfio and Tojeiro on the classification of constant sectional curvature hypersurfaces of and . 相似文献
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Jun O'Hara 《Mathematische Nachrichten》2023,296(2):797-810
We show that the regularized Riesz α-energy for smooth closed submanifolds M in blows up as M degenerates to have double points if . This gives theoretical foundation of numerical experiments to evolve surfaces to decrease the energy that have been carried out since the 90's. 相似文献
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Let Δ be a one-dimensional simplicial complex. Let be the Stanley–Reisner ideal of Δ. We prove that for all and all intermediate ideals J generated by and some minimal generators of , we have 相似文献
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We show that if is a one-parameter continuous semigroup of nonexpansive mappings acting on a complete locally compact geodesic space that satisfies some geometric properties, then there exists such that S converge uniformly on bounded sets of Y to ξ. In particular, our result applies to strictly convex bounded domains in or with respect to a large class of metrics including Hilbert's and Kobayashi's metrics. 相似文献
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Suppose that R is a local domain with fraction field K. If R is Henselian, then the R-adic topology over K refines the étale open topology. If R is regular, then the étale open topology over K refines the R-adic topology. In particular, the étale open topology over agrees with the -adic topology for any field L and . 相似文献
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Giovany M. Figueiredo Marcelo Montenegro Matheus F. Stapenhorst 《Mathematische Nachrichten》2023,296(10):4569-4609
We show the existence of a solution for an equation where the nonlinearity is logarithmically singular at the origin, namely, in with Dirichlet boundary condition. The function f has exponential growth, which can be subcritical or critical with respect to the Trudinger–Moser inequality. We study the energy functional corresponding to the perturbed equation , where is well defined at 0 and approximates . We show that has a critical point in , which converges to a legitimate nontrivial nonnegative solution of the original problem as . We also investigate the problem with replaced by , when the parameter is sufficiently large. 相似文献
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Inspired by some iterative algorithms useful for proving the real analyticity (or the Gevrey regularity) of a solution of a linear partial differential equation with real-analytic coefficients, we consider the following question. Given a smooth function defined on and given an increasing divergent sequence of positive integers such that the derivative of order of f has a growth of the type , when can we deduce that f is a function in the Denjoy–Carleman class ? We provide a positive result and show that a suitable condition on the gaps between the terms of the sequence is needed. 相似文献
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A. R. Mirotin 《Mathematische Nachrichten》2023,296(9):4108-4124
Necessary and sufficient conditions are given for the boundedness of Hausdorff operators on the generalized Hardy spaces , real Hardy space , , and for compact Abelian group G. Surprisingly, these conditions turned out to be the same for all groups and spaces under consideration. Applications to Dirichlet series are given. The case of the space of continuous functions on G and examples are also considered. 相似文献
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Aurélio Menegon 《Mathematische Nachrichten》2023,296(8):3481-3491
Let (X, 0) be the germ of either a subanalytic set or a complex analytic space , and let be a -analytic map-germ, with or , respectively. When , there is a well-known topological locally trivial fibration associated with f, called the Milnor–Lê fibration of f, which is one of the main pillars in the study of singularities of maps and spaces. However, when that is not always the case. In this paper, we give conditions which guarantee that the image of f is well-defined as a set-germ, and that f admits a Milnor–Lê fibration. We also give conditions for f to have the Thom property. Finally, we apply our results to mixed function-germs of type on a complex analytic surface with arbitrary singularity. 相似文献
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Roger Bielawski 《Mathematische Nachrichten》2023,296(1):122-129
We show that -invariant hypercomplex structures on (open subsets) of regular semisimple adjoint orbits in correspond to algebraic curves C of genus , equipped with a flat projection of degree k, and an antiholomorphic involution covering the antipodal map on . 相似文献
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We give a complete local classification of all Riemannian 3-manifolds admitting a nonvanishing Killing vector field T. We then extend this classification to timelike Killing vector fields on Lorentzian 3-manifolds, which are automatically nonvanishing. The two key ingredients needed in our classification are the scalar curvature S of g and the function , where Ric is the Ricci tensor; in fact their sum appears as the Gaussian curvature of the quotient metric obtained from the action of T. Our classification generalizes that of Sasakian structures, which is the special case when . We also give necessary, and separately, sufficient conditions, both expressed in terms of , for g to be locally conformally flat. We then move from the local to the global setting, and prove two results: in the event that T has unit length and the coordinates derived in our classification are globally defined on , we give conditions under which S completely determines when the metric will be geodesically complete. In the event that the 3-manifold M is compact, we give a condition stating when it admits a metric of constant positive sectional curvature. 相似文献
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We show that defines a birational map and has no fixed part for some bounded positive integer m for any -lc surface X such that is big and nef. For every positive integer , we construct a sequence of projective surfaces , such that is ample, for every i, , and for any positive integer m, there exists i such that has nonzero fixed part. These results answer the surface case of a question of Xu. 相似文献
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Jonas Baltes 《Mathematische Nachrichten》2023,296(7):2701-2714
We show that on every elliptic K3 surface there are rational curves such that , that is, of unbounded arithmetic genus. Moreover, we show that the union of the lifts of these curves to is dense in the Zariski topology. As an application, we give a simple proof of a theorem of Kobayashi in the elliptic case, that is, there are no globally defined symmetric differential forms. 相似文献
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We investigate the topological structures of Galois covers of surfaces of minimal degree (i.e., degree n) in . We prove that for , the Galois covers of any surfaces of minimal degree are simply-connected surfaces of general type. 相似文献
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