منابع مشابه
Regularity Properties of Equilibrium Configurations of Epitaxially Strained Elastic Films
We consider a variational model introduced in the physical literature to describe the epitaxial growth of an elastic film over a rigid substrate, when a lattice mismatch between the two materials is present. We establish the regularity of volume constrained local minimizers of the total energy, proving in particular the so called zero contact-angle condition between the film and the substrate.
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Geodesic rays of class C1,1 are constructed for any test configuration of a positive line bundle L → X, using resolution of singularities. The construction reduces to finding a subsolution of the corresponding Monge-Ampère equation. Geometrically, this is accomplished by the use a positive line bundle on the resolution which is trivial outside of the exceptional divisor.
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Begin with a set of four points in the real plane in general position. Add to this collection the intersection of all lines through pairs of these points. Iterate. Ismailescu and Radoičić (2003) showed that the limiting set is dense in the plane. We give doubly exponential upper and lower bounds on the number of points at each stage. The proof employs a variant of the Szemerédi-Trotter Theorem ...
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Associated to a projective arrangement of hyperplanes A ⊆ Pn is the module D(A), which consists of derivations tangent to A. We study D(A) when A is a configuration of lines in P. In this setting, we relate the deletion/restriction construction used in the study of hyperplane arrangements to elementary modifications of bundles. This allows us to obtain bounds on the Castelnuovo-Mumford regulari...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2018
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2017.10.009