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Full-Text Articles in Physical Sciences and Mathematics
Conformal Laplacian And Conical Singularities, Boris Botvinnik, Serge Preston
Conformal Laplacian And Conical Singularities, Boris Botvinnik, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
We study a behavior of the conformal Laplacian operator $\L_g$ on a manifold with \emph{tame conical singularities}: when each singularity is given as a cone over a product of the standard spheres. We study the spectral properties of the operator $\L_g$ on such manifolds. We describe the asymptotic of a general solution of the equation $\L_g u = Q u^{\alpha}$ with 1≤α≤n+2 near each singular point. In particular, we derive the asymptotic of the Yamabe metric near such singularity.
On The Evolution Of Simple Material Structures, Marek Elźanowski, Ernst Binz
On The Evolution Of Simple Material Structures, Marek Elźanowski, Ernst Binz
Mathematics and Statistics Faculty Publications and Presentations
The evolution of a distribution of material inhomogeneities is investigated by analyzing the evolution of the corresponding material connections. Some general geometric relations governing such evolutions are derived. These relations are then analyzed by looking at the restrictions imposed by the material symmetry group.