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Motivated by the quasi-local mass problem in general relativity, we study the rigidity of isometric immersions with the same mean curvature into a warped product space. As a corollary of our main result, two star-shaped hypersurfaces in a spatial Schwarzschild or AdS-Schwarzschild manifold with nonzero mass differ only by a rotation if they are isometric and have the same mean curvature. We also prove similar results if the mean curvature condition is replaced by an -curvature condition. 相似文献
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Tanja Vidaković-Koch Tamara Miličić Luka A. Živković Hoon Seng Chan Ulrike Krewer Menka Petkovska 《Current Opinion in Electrochemistry》2021
The nonlinear frequency response analysis (NFRA) can be seen as an extension of electrochemical impedance spectroscopy. NFRA gives a full and detailed representation of the system response and can establish a connection between model parameters and the experimentally observed phenomena. In this article, different theoretical NFRA approaches and the most recent application examples are discussed. A simple electrochemical example is used to showcase the benefits and disadvantages of analyzing the system response by using different approaches. In addition, it was shown how to extract experimental harmonic values and analyze them. 相似文献
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Tobias Kirschbaum Dr. Frank Rominger Prof. Dr. Michael Mastalerz 《Chemistry (Weinheim an der Bergstrasse, Germany)》2020,26(64):14560-14564
Since a few years, the interest in negatively-curved fused polycyclic aromatic hydrocarbons (PAHs) has significantly increased. Recently, the first chiral negatively-curved PAH with the topology of a monkey saddle was introduced. Herein the synthesis of its triaza congener is reported. The influence of this CH↔N exchange on photophysical and electrochemical properties is studied as well as the isomerization process of the enantiomers. The aza analogue has a significantly higher inversion barrier, which makes it easier to handle at room temperature. All experimental results are underpinned by theoretical DFT calculations. 相似文献
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Timothy Buttsworth 《Mathematische Nachrichten》2019,292(4):747-759
Let G be a three‐dimensional unimodular Lie group, and let T be a left‐invariant symmetric (0,2)‐tensor field on G. We provide the necessary and sufficient conditions on T for the existence of a pair consisting of a left‐invariant Riemannian metric g and a positive constant c such that , where is the Ricci curvature of g. We also discuss the uniqueness of such pairs and show that, in most cases, there exists at most one positive constant c such that is solvable for some left‐invariant Riemannian metric g. 相似文献
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Rongmu YAN 《数学年刊B辑(英文版)》2020,41(3):451-464
In this paper, the author establishs a real-valued function on K¨ahler manifolds by holomorphic sectional curvature under parallel translation. The author proves if such functions are equal for two simply-connected, complete K¨ahler manifolds, then they are holomorphically isometric. 相似文献
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In this paper we give sufficient conditions that guarantee the mean curvature flow with free boundary on a pinched cylinder develops a Type 2 curvature singularity. We additionally prove that Type 0 singularities may only occur at infinity. 相似文献
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Yuxin Wang Huafei Sun Shoudong Huang Yang Song 《Mathematical Methods in the Applied Sciences》2020,43(2):486-511
This paper focuses on using the first curvature κ(t) of trajectory to describe the stability of linear time-invariant system. We extend the results for two and three-dimensional systems (Wang, Sun, Song et al, arXiv:1808.00290) to n-dimensional systems. We prove that for a system , (a) if there exists a measurable set whose Lebesgue measure is greater than zero, such that or does not exist for any initial value in this set, then the zero solution of the system is stable; (b) if the matrix A is invertible, and there exists a measurable set whose Lebesgue measure is greater than zero, such that for any initial value in this set, then the zero solution of the system is asymptotically stable. 相似文献