A curvature-area inequality for planar curves with cusps is derived. Using this inequality, the total (Lipschitz-Killing) curvature of a map with stable singularities of a closed surface into the plane is shown to be bounded below by the area of the map divided by the square of the radius of the smallest ball containing the image of the map. This latter result fills the gap in Santaló's proof of a similar estimate for surface maps into $\mathbf{R}^n$, $n>2$
AbstractIn this paper we investigate Σ1,0-maps of closed surfaces into the plane, specifically, the ...
This work is devoted to the investigation of the basic relationship between the geometric shape of a...
In this thesis, we give a lower bound on the areas of small geodesic balls in an immersed hypersurfa...
In this paper we provide an estimate from above for the value of the relaxed area function...
In this paper we provide an estimate from above for the value of the relaxed area functional A¯(u, Ω...
We prove that finite area isolated singularities of surfaces with constant positive curvature K> ...
We show that the total area of two distinct Gaussian curvature 1 surfaces with the same conformal fa...
Given a smooth simply connected planar domain, the area is bounded away from zero in terms of the ma...
Let M be an embedded strictly stable constant mean curvature surface, and S a surface with the same ...
In this thesis, we give curvature estimates for strongly stable constant mean curvature surfaces in ...
Abstract. It is well known that the area U of the triangle formed by three tangents to a parabola X ...
We prove an equality for the curvature function of a simple and closed curve on the plane. This equa...
We investigate a geometric inequality that states that in R2, the mean curvature of a closed curve γ...
We show that a smooth unknotted curve in R^3 satisfies an isoperimetric inequality that bou...
Based on computing spherical lengths of polygonal curves and spherical areas of domains bounded by p...
AbstractIn this paper we investigate Σ1,0-maps of closed surfaces into the plane, specifically, the ...
This work is devoted to the investigation of the basic relationship between the geometric shape of a...
In this thesis, we give a lower bound on the areas of small geodesic balls in an immersed hypersurfa...
In this paper we provide an estimate from above for the value of the relaxed area function...
In this paper we provide an estimate from above for the value of the relaxed area functional A¯(u, Ω...
We prove that finite area isolated singularities of surfaces with constant positive curvature K> ...
We show that the total area of two distinct Gaussian curvature 1 surfaces with the same conformal fa...
Given a smooth simply connected planar domain, the area is bounded away from zero in terms of the ma...
Let M be an embedded strictly stable constant mean curvature surface, and S a surface with the same ...
In this thesis, we give curvature estimates for strongly stable constant mean curvature surfaces in ...
Abstract. It is well known that the area U of the triangle formed by three tangents to a parabola X ...
We prove an equality for the curvature function of a simple and closed curve on the plane. This equa...
We investigate a geometric inequality that states that in R2, the mean curvature of a closed curve γ...
We show that a smooth unknotted curve in R^3 satisfies an isoperimetric inequality that bou...
Based on computing spherical lengths of polygonal curves and spherical areas of domains bounded by p...
AbstractIn this paper we investigate Σ1,0-maps of closed surfaces into the plane, specifically, the ...
This work is devoted to the investigation of the basic relationship between the geometric shape of a...
In this thesis, we give a lower bound on the areas of small geodesic balls in an immersed hypersurfa...