共查询到20条相似文献,搜索用时 903 毫秒
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In this paper, we study geometry of totally real minimal surfaces in the complex hyperquadric , and obtain some characterizations of the harmonic sequence generated by these minimal immersions. For totally real flat surfaces that are minimal immersed in both and , we determine them for , and give a classification theorem when they are Clifford solutions. 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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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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This paper will establish the asymptotic behavior of an anisotropic area-preserving flow which shows the existence of smooth solutions of the planar Minkowski problem for . 相似文献
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Vicente Lorenzo 《Mathematische Nachrichten》2023,296(6):2503-2512
In this note, the geography of minimal surfaces of general type admitting -actions is studied. More precisely, it is shown that Gieseker's moduli space contains surfaces admitting a -action for every admissible pair such that or . The examples considered allow to prove that the locus of Gorenstein stable surfaces is not closed in the KSBA-compactification of Gieseker's moduli space for every admissible pair such that . 相似文献
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A Banach space X has property (K), whenever every weak* null sequence in the dual space admits a convex block subsequence so that as for every weakly null sequence in X; X has property if every weak* null sequence in admits a subsequence so that all of its subsequences are Cesàro convergent to 0 with respect to the Mackey topology. Both property and reflexivity (or even the Grothendieck property) imply property (K). In this paper, we propose natural ways for quantifying the aforementioned properties in the spirit of recent results concerning other familiar properties of Banach spaces. 相似文献
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For a positive integer N, let be the modular curve over and its Jacobian variety. We prove that the rational cuspidal subgroup of is equal to the rational cuspidal divisor class group of when for any prime p and any squarefree integer M. To achieve this, we show that all modular units on can be written as products of certain functions , which are constructed from generalized Dedekind eta functions. Also, we determine the necessary and sufficient conditions for such products to be modular units on under a mild assumption. 相似文献
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We prove that the kth Gaussian map is surjective on a polarized unnodal Enriques surface with . In particular, as a consequence, when , we obtain the surjectivity of the kth Gauss-Prym map , with , on smooth hyperplane sections . In case , it is sufficient to ask . 相似文献
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Ferenc Weisz 《Mathematische Nachrichten》2023,296(4):1687-1705
Let be a measurable function defined on and . In this paper, we generalize the Hardy–Littlewood maximal operator. In the definition, instead of cubes or balls, we take the supremum over all rectangles the side lengths of which are in a cone-like set defined by a given function ψ. Moreover, instead of the integral means, we consider the -means. Let and satisfy the log-Hülder condition and . Then, we prove that the maximal operator is bounded on if and is bounded from to the weak if . We generalize also the theorem about the Lebesgue points. 相似文献
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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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We obtained order estimates for the entropy numbers of the Nikol'skii–Besov classes of functions with mixed smoothness in the metric of the space of quasi-continuous functions . We also showed that for , , , , the estimate of the corresponding asymptotic characteristic is exact in order. 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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Yu Yang 《Mathematische Nachrichten》2023,296(8):3740-3781
In this paper, we study anabelian geometry of curves over algebraically closed fields of positive characteristic. Let be a pointed stable curve over an algebraically closed field of characteristic and the admissible fundamental group of . We prove that there exists a group-theoretical algorithm, whose input datum is the admissible fundamental group , and whose output data are the topological and the combinatorial structures associated with . This result can be regarded as a mono-anabelian version of the combinatorial Grothendieck conjecture in the positive characteristic. Moreover, by applying this result, we construct clutching maps for moduli spaces of admissible fundamental groups. 相似文献
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We study the spectral heat content for a class of open sets with fractal boundaries determined by similitudes in , , with respect to subordinate killed Brownian motions via -stable subordinators and establish the asymptotic behavior of the spectral heat content as for the full range of . Our main theorems show that these asymptotic behaviors depend on whether the sequence of logarithms of the coefficients of the similitudes is arithmetic when , where is the interior Minkowski dimension of the boundary of the open set. The main tools for proving the theorems are the previous results on the spectral heat content for Brownian motions and the renewal theorem. 相似文献
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Young Jin Suh 《Mathematische Nachrichten》2023,296(8):3630-3651
We introduce the notion of harmonic curvature for real hypersurfaces in the complex quadric . First, we prove that the unit normal vector field N on real hypersurfaces in with harmonic curvature is singular, that is, -principal or -isotropic. Next by using a new notion of cyclic semiparallel Ricci tensor, we give a new result on real hypersurfaces with harmonic curvature and constant mean curvature in . 相似文献
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We study vector bundles on flag varieties over an algebraically closed field k. In the first part, we suppose to be the Grassmannian parameterizing linear subspaces of dimension d in , where k is an algebraically closed field of characteristic . Let E be a uniform vector bundle over G of rank . We show that E is either a direct sum of line bundles or a twist of the pullback of the universal subbundle or its dual by a series of absolute Frobenius maps. In the second part, splitting properties of vector bundles on general flag varieties in characteristic zero are considered. We prove a structure theorem for bundles over flag varieties which are uniform with respect to the ith component of the manifold of lines in . Furthermore, we generalize the Grauert–Mlich–Barth theorem to flag varieties. As a corollary, we show that any strongly uniform i-semistable bundle over the complete flag variety splits as a direct sum of special line bundles. 相似文献