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We prove that if the Gauss map of a minimal surface immersed in Rm omits a generic hypersurface of large enough degree, then it must be constant.
Generalized pairs are a natural structure in birational geometry that first appeared in Kodaira’s canonical bundle formula for elliptic fibrations. They were formally introduced by Birkar and Zhang in...
The well-known Simons cone suggests that singularities may exist in a stable minimal hypersurface in Riemannian manifolds of dimension greater than 7, locally modeled on stable minimal hypercones. It ...
In this paper, we study VC-minimal theories and explore related concepts. We first define the notion of convex orderablity and show that this lies strictly between VCminimality and dp-minimality. To...
We show that any family of sets uniformly definable in an ominimal structure has an extended compression scheme of size equal to the number of parameters in the defining formula.
We prove that if M is any model of a trivial, weakly minimal theory, then the elementary diagram T(M) eliminates quantifiers down to Boolean combinations of certain existential formulas.
We show the existence of a trivial, strongly minimal (and thus uncountably categorical) theory for which the prime model is computable and each of the other countable models computes 0 00. This res...
We prove that if M is any model of a trivial, strongly minimal theory, then the elementary diagram Th(MM ) is a model complete LM -theory. We conclude that all countable models of a trivial, strong...
For a countable, weakly minimal theory T, we show that the SchröderBernstein property (any two elementarily bi-embeddable models are isomorphic) is equivalent to each of the following: 1. For ...
We consider inexact linear equations y ≈ Φα where y is a given vector in R n , Φ is a given n by m matrix, and we wish to find an α0, which is sparse and gives an approximate solution, obey...
We consider linear equations y = Φα where y is a given vector in R n , Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ Rm. We suppose that the columns of Φ are normalized ...
In 1971 Laver proved the following result, confirming a long-standing conjecture of Fraïssé. Theorem 1.1 [10]. If Li (i < ω) is a sequence of σ-scattered linear orders, then there exist i < j suc...
This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that pro...
Entire Solutions of the Allen-Cahn Equation and Complete Embedded Minimal Surfaces of Finite Total Curvature in R3.
The inclusion-exclusion formula (IEF) is a fundamental tool for evaluating network reliability with known minimal paths or minimal cuts. However, the formula contains many pairs of terms which cancel....

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