Related papers: On integral boxes of minimal surface
We have derived an analytical formulation for estimating the volume of geometries enclosed by implicitly defined surfaces. The novelty of this work is due to two aspects. First we provide a general analytical formulation for all…
We compute the depth and (give bounds for) the regularity of generalized binomial edge ideals associated with generalized block graphs.
We consider a rational elliptic surface with a relatively minimal fibration. We compute the number of integral sections in the above rational elliptic surface. As an application, we obtain an estimate of polynomial solutions of some…
In this article a new upper bounds for the multiple trigonometrical integrals are found. The method of the work based on a new method of estimation for the areas of algebraic surfaces.
We derive integral and sup-estimates for the curvature of stably marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature…
Geometrical objects with integral sides have attracted mathematicians for ages. For example, the problem to prove or to disprove the existence of a perfect box, that is, a rectangular parallelepiped with all edges, face diagonals and space…
We estimate the maximal number of integral points which can be on a convex arc in the plane with given length, minimal radius of curvature and initial slope.
We establish central limit theorems for natural volumes of random inscribed polytopes in projective Riemannian or Finsler geometries. In addition, normal approximation of dual volumes and the mean width of random polyhedral sets are…
We write down estimates for the surface area, and more generally, integral mean curvatures of an ellipsoid E in n-dimensional Euclidean space in terms of the lengths of the major semi-axes. We give applications to estimating the area of…
We give an attempt to build a classification of planar integral point sets. For two obtained classes, we provide general constructions of upper bounds for minimal diameter of integral point sets in higher dimensions of certain cardinality.…
We give an elementary proof that, for a closed manifold with an integral-integral affine structure, its total volume and number of integral points coincide. The proof uses rational Ehrhart theory and elementary Fourier analysis to estimate…
Intrinsic volumes are fundamental geometric invariants generalizing volume, surface area, and mean width for convex bodies. We establish a unified Laplace-Grassmannian representation for intrinsic and dual volumes of convex polynomial…
In this survey article we will consider universal lower bounds on the volume of a Riemannian manifold, given in terms of the volume of lower dimensional objects (primarily the lengths of geodesics). By `universal' we mean without curvature…
In a given hypercube, draw grid lines parallel to the edges, and consider all hypercuboids (or hypercubes) whose edges are lying on the grid lines or the boundary. We find the limit of the value of the ratio of the arithmetic mean of the…
The aim of this paper is to give an upper bound for the intrinsic diameter of a surface with boundary immersed in a conformally flat three dimensional Riemannian manifold in terms of the integral of the mean curvature and of the length of…
The oloid is the convex hull of two circles with equal radius in perpendicular planes so that the center of each circle lies on the other circle. We calculate the mean width of the oloid in two ways, first via the integral of mean…
We prove qualitative estimates on the total curvature of closed minimal hypersurfaces in closed Riemannian manifolds in terms of their index and area, restricting to the case where the hypersurface has dimension less than seven. In…
In this short paper, an older Efron's result is extended to obtain a cutting plane integral formula for the mean volume of a random simplex in any d dimensions.
Given a closed connected manifold smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we estimate the intrinsic diameter of the submanifold in terms of its mean curvature field integral. On…
We use the theory of calibrations to write the equation of a minimal volume vector field on a given Riemann surface.