9,208 research outputs found
Frobenius 3-Folds via Singular Flat 3-Webs
We give a geometric interpretation of weighted homogeneous solutions to the
associativity equation in terms of the web theory and construct a massive
Frobenius 3-fold germ via a singular 3-web germ satisfying the following
conditions: 1) the web germ admits at least one infinitesimal symmetry, 2) the
Chern connection form is holomorphic, 3) the curvature form vanishes
identically
Exact constants in Poincare type inequalities for functions with zero mean boundary traces
In the paper, we investigate Poincare type inequalities for the functions
having zero mean value on the whole boundary of a Lipschitz domain or on a
measurable part of the boundary. We derive exact and easily computable
constants for some basic domains (rectangles, cubes, and right triangles). In
the last section, we derive an a estimate of the difference between the exact
solutions of two boundary value problems. Constants in Poincare type
inequalities enter these estimates, which provide guaranteed a posteriori error
control.Comment: A gap in the proof of Theorem 3.2 is fixed; 19 pages, 3 figure
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