In this paper, we give several applications of the discrete game approach to partial differential equations. We first present a rigorous game-theoretic proof of fattening phenomenon for motion by curvature with figure-eight shaped initial curves without using parabolic PDE theory. The proof is based on a comparison between the game value and its inverse one. Accompanied with the example of figu...

This is the first of two papers where we address and partially confirm a conjecture of Deser and Schwimmer, originally postulated in high energy physics, [10]. The objects of study are scalar Riemannian quantities constructed out of the curvature and its covariant derivatives, whose integrals over compact manifolds are invariant under conformal changes of the underlying metric. Our main conclus...

We study the boundary measures of compact subsets of the d-dimensional Euclidean space, which are closely related to Federer’s curvature measures. We show that they can be computed efficiently for point clouds and suggest that these measures can be used for geometric inference. The main contribution of this work is the proof of a quantitative stability theorem for boundary measures using tools ...

In this paper, we introduce iterative mean and median filtering schemes for smoothing noisy 3D shapes given as triangle meshes. Our main idea consists of applying mean and median filtering schemes to mesh normals and then update the mesh vertex position in order to fit the mesh to the modified normals. We also give a quantitative evaluation of the proposed mesh filtering schemes and compare the...

This paper presents an algebraically extended 2D image representation. Combining methods of tensor algebra, monogenic signal and quadrature filter, this novel image representation can be derived as the monogenic extension of a curvature tensor. From it, the monogenic signal and the monogenic curvature signal for modeling intrinsically one and two dimensional (i1D/i2D) structures are obtained as...

We develop a qualitative geometric approach to swimming at low Reynolds number which avoids solving differential equations and uses instead landscape figures of two notions of curvatures: The swimming curvature and the curvature derived from dissipation. This approach gives complete information for swimmers that swim on a line without rotations and gives the main qualitative features for genera...

Relatively extremal knots are the relative minima of the ropelength functional in the C1 topology. They are the relative maxima of the thickness (normal injectivity radius) functional on the set of curves of …xed length, and they include the ideal knots. We prove that a C1;1 relatively extremal knot in Rn either has constant maximal (generalized) curvature, or its thickness is equal to half of ...

Urethral stricture is a common urological pathology with a high recurrence rate after treatment. Urethral manipulations are among its main causes. In this paper, urethral stricture developed secondary to urethral catheterization and was treated with cold-knife internal urethrotomy and the Otis urethrotomy procedure. During the follow-up period, severe ventral penile curvature preventing sexual ...

In this paper, we show that an $L_1$-2-type surface in the three-dimensional hyperbolic space $H^3subset R^4_1$ either is an open piece of a standard Riemannian product $ H^1(-sqrt{1+r^2})times S^{1}(r)$, or it has non constant mean curvature, non constant Gaussian curvature, and non constant principal curvatures.

materials and methods: one hundred and thirty five mesial root canals of mandibular first and second molar teeth were selected. access cavities were prepared. after inserting a k-file size #10 into each canal, radiographs were taken. canal curvature was determined by measuring the schneider angle, canal access angle, as well as the canal radius, length, height and curvature starting distance on...