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The heat equation shrinks embedded plane curves to round points
Soit C(•,0):S 1 →R 2 une courbe lisse plongee dans le plan. Alors C:S 1 ×[0,T)→R 2 existe en satisfaisant δC/δt=K•N, ou K est la courbure de C, et N est son vecteur unite normal entrant. C(•,t) est
The formation of singularities in the harmonic map heat flow
is called the harmonic map heat flow. In their paper [3], Eells and Sampson introduced this flow and proved that if the target N has non-positive sectional curvature, then the solution exists for all
Solvgroups are not almost convex
We show that no cocompact discrete group based on solvgeometry, Sol, is almost convex. This reflects the geometry of Sol, and implies that the Cayley graph of a cocompact discrete group based on Sol
Models for Free Nilpotent Lie Algebras
If a Lie algebra g can be generated by M of its elements E1, . . . , EM , and if any other Lie algebra generated by M other elements F1, . . . , FM is a homomorphic image of g under the map Ei → Fi,
Orientation maps: techniques for visualizing rotations (a consumer's guide)
This paper investigates the suitability of various techniques of visualizing the set of possible orientations of a rigid three-dimensional object in a topological space with three degrees of freedom.