Related papers: Beyond Mumford's theorem on normal surfaces

In the article it was shown the convergence of special integral of two dimensional Terry's problem. Main tools of the article are an investigation of real algebraic varieties and estimations of areas of algebraic surfaces.

Normed division and Clifford algebras have been extensively used in the past as a mathematical framework to accommodate the structures of the standard model and grand unified theories. Less discussed has been the question of why such…

This paper discusses an ordinary homogeneous differential equation of the second order with constant real-valued coefficients. The solution of this equation has to satisfy additional conditions. The first of the conditions stems from the…

A Brief review on the physics beyond the Standard Model.

We show well-posedness for the parabolic Anderson model on $2$-dimensional closed Riemannian manifolds. To this end we extend the notion of regularity structures to curved space, and explicitly construct the minimal structure required for…

Minkowski's 2nd theorem in the Geometry of Numbers provides optimal upper and lower bounds for the volume of a $o$-symmetric convex body in terms of its successive minima. In this paper we study extensions of this theorem from two different…

In this speculative analysis, interdimensionality is introduced as the (co)existence of universes embedded into larger ones. These interdimensional universes may be isolated or intertwined, suggesting a variety of interdimensional intrinsic…

In metaphysics, there are a number of distinct but related questions about the existence of "further facts" -- facts that are contingent relative to the physical structure of the universe. These include further facts about qualia, personal…

Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.

The following are notes on the geometry of the bidisk. In particular, we examine the properties of equidistant surfaces in the bidisk.

In this paper we prove a conjecture on the dimension of linear systems, with base points of multiplicity 2 and 3, on an Hirzebruck surface.

In this paper we first give a Bonnet theorem for conformal Lagrangian surfaces in complex space forms, then we show that any compact Lagrangian surface in the complex space form admits at most one other global isometric Lagrangian surface…

After the surface theory of M\"obius geometry, this study concerns a pair of conformally immersed surfaces in $n$-sphere. Two new invariants $\theta$ and $\rho$ associated with them are introduced as well as the notion of touch and…

An expression for the first variation of the area functional of the second fundamental form is given for a hypersurface in a semi-Riemannian space. The concept of the "mean curvature of the second fundamental form" is then introduced. Some…

The linear isometries between weighted Banach spaces of continuous functions are considered. Some of well known theorems on isometries between spaces of continuous functions are proved and stated, but all they are in an appropriate form. In…

Quantum physics has intrigued scientists and philosophers alike, because it challenges our notions of reality and locality--concepts that we have grown to rely on in our macroscopic world. It is an intriguing open question whether the…

It is conjectured since long that for any convex body $P\subset \mathbb{R}^n$ there exists a point in its interior which belongs to at least $2n$ normals from different points on the boundary of $P$. The conjecture is known to be true for…

This survey is an invitation to recent developments in higher dimensional birational geometry.

We define two transforms between minimal surfaces with non-circular ellipse of curvature in the 5-sphere, and show how this enables us to construct, from one such surface, a sequence of such surfaces. We also use the transforms to show how…

We establish a half-space theorem \`a la Hoffman and Meeks for nonlocal minimal surfaces. Differently from the classical case, our result holds in every dimension.