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On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold

John C. Taylor (1978)

Annales de l'institut Fourier

The Martin compactification of a bounded Lipschitz domain D R n is shown to be D for a large class of uniformly elliptic second order partial differential operators on D .Let X be an open Riemannian manifold and let M X be open relatively compact, connected, with Lipschitz boundary. Then M is the Martin compactification of M associated with the restriction to M of the Laplace-Beltrami operator on X . Consequently an open Riemannian manifold X has at most one compactification which is a compact Riemannian...

On the maximum principle for principal curvatures

Nina Ivochkina (1996)

Banach Center Publications

The paper contains the estimates from above of the principal curvatures of the solution to some curvature equations. A correction of the author's previous argument is presented.

On the measurability of sets of pairs of intersecting nonisotropic straight lines of type beta in the simply isotropic space

Adrijan Varbanov Borisov, Margarita Georgieva Spirova (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The measurable sets of pairs of intersecting non-isotropic straight lines of type β and the corresponding densities with respect to the group of general similitudes and some its subgroups are described. Also some Crofton-type formulas are presented.

On the motion of a curve by its binormal curvature

Jerrard, Robert L., Didier Smets (2015)

Journal of the European Mathematical Society

We propose a weak formulation for the binormal curvature flow of curves in 3 . This formulation is sufficiently broad to consider integral currents as initial data, and sufficiently strong for the weak-strong uniqueness property to hold, as long as self-intersections do not occur. We also prove a global existence theorem in that framework.

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