Related papers: $T$-convexly valued o-minimal fields are definably…

Consider a domain D in R^3 which is convex (possibly all R^3) or which is smooth and bounded. Given any open surface M, we prove that there exists a complete, proper minimal immersion f : M --> D. Moreover, if D is smooth and bounded, then…

Let R be a sufficiently saturated o-minimal expansion of a real closed field, let O be the convex hull of the rationals in R, and let st: O^n \to \mathbb{R}^n be the standard part map. For X \subseteq R^n define st(X):=st(X \cap O^n). We…

We partially resolve a conjecture of Meeks on the asymptotic behavior of minimal surfaces in $\mathbb{R}^3$ with quadratic area growth.

We show that every complete $n$-vertex simple topological graph contains a topological subgraph on at least $(\log n)^{1/4 - o(1)}$ vertices that is weakly isomorphic to the complete convex geometric graph or the complete twisted graph.…

In this short note we prove that if X is a separably rationally connected variety over an algebraically closed field of positive characteristic, then H^1(X, O_X)=0.

In [4] we developed the theory of positive cones on finite-dimensional simple algebras with involution, inspired by the classical Artin-Schreier theory of orderings on fields, and based on the notion of signatures of hermitian forms [1]. In…

We study d-minimal expansions of ordered fields, and dense pairs thereof. We also consider other generalizations of o-minimality.

We provide a remarkably compact proof that spherically symmetric neutral black holes cannot support static nonminimally coupled massless scalar fields. The theorem is based on causality restrictions imposed on the energy-momentum tensor of…

This paper builds fundamental perfect fields of positive characteristic and shows the structure of perfect fields that a field of positive characteristic is a perfect field if and only if it is an algebraic extension of a fundamental…

Given a logarithmic $1$-form on the snc locus of a log canonical surface pair $(X, D)$ over a perfect field of characteristic $p \ge 7$, we show that it extends with at worst logarithmic poles to any resolution of singularities. We also…

We reconsider some subtle points concerning the relativistic treatment of the gravitational fields generated by spherically symmetric structures.

We prove that strictly mean convex toroids contain infinitely many (geometrically distinct) embedded free boundary minimal M\"obius bands as well as infinitely many embedded free boundary minimal annuli. The surfaces in both families are…

For $(K,v)$ a Henselian valued field, let $\theta\in\overline{K}$ with minimal polynomial $F$ over $K$. Okutsu sequences of $\theta$ have been defined only when the extension $K(\theta)/K$ is defectless. In this paper, we extend this…

In this paper we examine different aspects of the geometry of closed conformal vector fields on Riemannian manifolds. We begin by getting obstructions to the existence of closed conformal and nonparallel vector fields on complete manifolds…

Let $Z_{r, R}$ be the space of continuous functions on the annulus $B_{r, R}$ in $\mathbb C^n$ whose $\lambda$-twisted spherical mean, in the set up of the M\'{e}tivier group, vanishes over the spheres $S_s(z)\subset B_{r, R} $ with ball…

We prove that a smooth scheme of dimension $n$ over a perfect field is A^1-weakly equivalent to a point if it is A^1-n-connected. We also prove an excision result for A^1-homotopy sheaves over a perfect field.

This paper is concerned with algebraic geometry over complete discretely valued fields $K$ of equicharacteristic zero. Several results are given including: the canonical projection $K^{n} \times K\mathbb{P}^{m} \longrightarrow K^{n}$ and…

Duality for complete discrete valuation fields with perfect residue field with coefficients in (possibly p-torsion) finite flat group schemes was obtained by Begueri, Bester and Kato. In this paper, we give another formulation and proof of…

In this paper we establish that if a Tychonoff space $X$ is \v{C}ech-complete then the space $O_\tau(X)$ of all $\tau$-smooth order-preserving, weakly additive and normed functionals is also \v{C}ech-complete

This paper introduces a novel approach to the axiomatic theory of quadratic forms. We work internally in a category of certain partially ordered sets, subject to additional conditions which amount to a strong form of local presentability.…