Mathematische Nachrichten最新文献

Fraser–Sargent surfaces are free boundary minimal surfaces in the four-dimensional unit Euclidean ball. Extended infinitely they define immersed minimal surfaces in the Euclidean space. The parts of these surfaces outside the ball are exterior-free boundary minimal surfaces. We prove that they are stable. Independently of it, we find an upper bound on the index of Fraser–Sargent surfaces inside the ball. Also, we provide computational experiments and state a conjecture about an improved index lower bound of the orientable cover of Fraser–Sargent surfaces inside the ball. Finally, based on a similar computational experiment for infinitely extended Fraser–Sargent surfaces, we state a conjecture about their index.

On real hypersurafces of the Kähler surface $��S^2�\times �S^2�$ and $��H^2�\times �H^2�$, there are three typical operators: the shape operator, the structure Lie operator, and the contact Lie operator. In this paper, we study real hypersurfaces in $��S^2�\times �S^2�$ and $��H^2�\times �H^2�$ related to these operators. As the main results, we classify real hypersurfaces of both $��S^2�\times �S^2�$ and $��H^2�\times �H^2�$

Cordes' characterization of Heisenberg-smooth operators bridges a gap between the theory of pseudo-differential operators and quantum harmonic analysis (QHA). We give a new proof of the result by using the phase-space formalism of QHA. Our argument is flexible enough to generalize Cordes' result in several directions: (1) we can admit general quantization schemes, (2) allow for other phase-space geometries, (3) obtain Schatten-class analogs of the result, and (4) are able to characterize precisely ‘Heisenberg-analytic’ operators. For (3), we use QHA to derive Schatten versions of the Calderón–Vaillancourt theorem, which might be of independent interest.

In this paper, the approximation of Dirac operators with general $�\delta$-shell potentials supported on $�C^2$-curves in $�R^2$ or $�C^2$-surfaces in $�R^3$, which may be bounded or unbounded, is studied. It is shown under suitable conditions on the weight of the $�\delta$-interaction that a family of Dirac operators with regular, squeezed potentials converges in the norm resolvent sense to the Dirac operator with the $�\delta$-shell interaction.

This paper is dedicated to the classification of uniform vector bundles of rank $��d�+�1�$ over the Grassmannian $��G�(�d�,�n�)�$ ($��2�\le �d�\le �n�-�d�$) over an algebraically closed field in positive characteristics. Specifically, we show that all uniform vector bundles with rank $��d�+�1�$ over $��G�(�d�,�n�)�$ are homogeneous.

The aim of this paper is to establish the boundedness of multiparameter singular integral operators associated with Zygmund dilations on product weighted Hardy spaces in the three-parameter setting. Additionally, we show that this class of operators are bounded on product Hardy spaces associated with ball quasi-Banach function spaces by employing the Rubio de Francia extrapolation technique. The generality of our result is illustrated by their applicability to concrete function spaces such as product Herz spaces and weighted product Morrey spaces. Even in these specific cases, the application yields entirely new results.

In this paper, we develop a new approach to investigation of the uniform stability for inverse spectral problems. We consider the non-self-adjoint Sturm–Liouville problem that consists in the recovery of the potential and the parameters of the boundary conditions from the eigenvalues and the generalized weight numbers. The special case of simple eigenvalues, as well as the general case with multiple eigenvalues, is studied. We find various subsets in the space of spectral data, on which the inverse mapping is Lipschitz continuous, and obtain the corresponding unconditional uniform stability estimates. Furthermore, the conditional uniform stability of the inverse problem under a priori restrictions on the potential is studied. In addition, we prove the uniform stability of the inverse problem by the Cauchy data, which are convenient for numerical reconstruction of the potential and for applications to partial inverse problems.

We study invariant Einstein metrics and Einstein–Randers metrics on the Stiefel manifold $��V_k�R^n�=�\mathrm{SO}��\left(�n�\right)��/�\mathrm{SO}��(�n�-�k�)��$. We use a characterization for (nonflat) homogeneous Einstein–Randers metrics as pairs of (nonflat) homogeneous Einstein metrics and invariant Killing vector fields. It is well known that, for Stiefel manifolds the isotropy representation contains equivalent summands, so a complete description of invariant metrics is difficult. We prove, by assuming additional symmetries, that the Stiefel manifolds $��V_{�1�+�k�}�R^{�1�+�2�k�}���(�k�>�2�)��$ and $��V_6�R^n���(�n�\ge �8�)��$