Prescribed curvature equationsIn this paper, we study the Dirichlet problem for a class of prescribed curvature equations in Minkowski space. We prove the existence of smooth spacelike hypersurfaces with a class of prescribed curvature and general boundary data based on establishing thea prioriC2...
rescaling the metricby constants, there is no sign restriction on the scalar curvature in the two remaining cases in Table1that are left empty. The scalar curvature of warped product type metrics are also studied in [13,14,15,16,17,18,27,44,53]. ...
Druet, O.: Generalized scalar curvature type equations on compact Riemannian manifolds. Proc. Roy. Soc. Edinb. Sect. A 130, 767–788 (2000) Article MathSciNet Google Scholar Fan, H., Liu, X.: Multiple positive solutions to a class of quasi-linear elliptic equations involving critical Sobo...
The local radius of the grain curvature in the vicinity of the contact, which was introduced and adopted by Cole and Peters (2007) and Sandeep and Senetakis (2018b), was taken as R in the analysis. Due to geometrical irregularities of real sand grains, the local radius can be quite ...
A machine-learned spin-lattice interatomic potential (MSLP) for magnetic iron is developed and applied to mesoscopic scale defects. It is achieved by augmenting a spin-lattice Hamiltonian with a neural network term trained to descriptors representing a m
Weyl semimetals (WSMs) are a recent addition to the family of topological materials, and the physical realization of heterojunctions between different types of WSMs is challenging. Here, we use electrical components to create topoelectrical (TE) circuits
[182]Caffarelli, Luis A.; Huang, QingboEstimates in the generalized Campanato-John-Nirenberg spaces for fully nonlinear elliptic equations.Duke Math. J.118(2003), no. 1, 1--17. [181]Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S.Stefan-like problems with curvature.J. Geom. Anal.13...
Enlightenment hegemony over the Western intellectual outlook, which can be summarized briefly as follows: that there exists an external world, whose properties are independent of any individual human being and indeed of humanity as a whole; that these properties are encoded in ``eternal'' physical ...
The local curvature κ(x) is calculated at each marker point x by using the osculator circle defined by x and its two neighbours. Thus, it should be exact when the interface Σ is a circle of radius R where the constant curvature equals κ=1/R or κ=2/R for a sphere in 3-D. It...
However, the Riemannian geometry is an arbi- trary request and in general a manifold is characterized by three fundamental geometrical objects: the curvature R, the torsion T and the non-metricity Q [1]. As a consequence, different theories of gravity can be built according to the properties...