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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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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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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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Lê Vǎn Thành 《Mathematische Nachrichten》2023,296(1):402-423
Li, Qi, and Rosalsky (Trans. Amer. Math. Soc., 368 (2016), no. 1, 539–561) introduced a refinement of the Marcinkiewicz–Zygmund strong law of large numbers (SLLN), the so-called -type SLLN, where and . They obtained sets of necessary and sufficient conditions for this new type SLLN for two cases: , , and . Results for the case where and remain open problems. This paper gives a complete solution to these problems. We consider random variables taking values in a real separable Banach space , but the results are new even when is the real line. Furthermore, the conditions for a sequence of random variables satisfying the -type SLLN are shown to provide an exact characterization of stable type p Banach spaces. 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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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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Ryoji Shimizu 《Mathematische Nachrichten》2023,296(7):3026-3033
Let K be a number field and S a set of primes of K. We write for the maximal extension of K unramified outside S and for its Galois group. In this paper, we answer the following question under some assumptions: “For , let be a number field, a (sufficiently large) set of primes of and an isomorphism. Is σ induced by a unique isomorphism between and ?” Here, the main assumption is about the Dirichlet density of . 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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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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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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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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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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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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