相关论文: A Minimax Lemma and its Applications
We establish some new common fixed point theorems of single-valued and multivalued mappings operating between complete ordered locally convex spaces under weaker assumptions. As an application, we prove a new minimax theorem of existence of…
We consider the minimal model program for varieties that are not Q-factorial. We show that, in many cases, its steps are simpler than expected. In particular, all flips are 1-complemented. The main applications are to log terminal…
We present a new, easy, and elementary proof of Jensen's Theorem on the uniqueness of infinity harmonic functions. The idea is to pass to a finite difference equation by taking maximums and minimums over small balls.
Wedderburn's theorem on the structure of finite dimensional semisimple algebras is proved by using minimal prerequisites.
Given $n \times n$ real symmetric matrices $A_1, \dots, A_m$, the following {\it spectral minimax} property holds: $$\min_{X \in \mathbf{\Delta}_n} \max_{y \in S_m} \sum_{i=1}^m y_iA_i \bullet X=\max_{y \in S_m} \min_{X \in…
In this note we answer a question concerning lineability of the set of non-absolutely summing operators.
The goal of this article is to prove the comparison theorem between algebraic and topological nearby cycles of a morphism without slopes. We prove in particular that for a family of holomorphic functions without slopes, if we iterate…
A min-max formula is proved for the minimum of an integer-valued separable discrete convex function where the minimum is taken over the set of integral elements of a box total dual integral (box-TDI) polyhedron. One variant of the theorem…
We propose a new formulation of a vanishing theorem for surfaces. Although this vanishing theorem follows easily from the well-known Kawamata--Viehweg vanishing theorem, it turns out to be remarkably useful. In particular, it is sufficient…
In this paper, we present new applications of our general minimax theorems. In particular, one of them concerns the multiplicity of global minima for the integral functional of the Calculus of Variations.
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…
We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.
Many economic theory models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. We provide a principled framework for scaling results from such models by removing these finiteness…
We apply the local removable singularity theorem for minimal laminations and the local picture theorem on the scale of topology to obtain two descriptive results for certain possibly singular minimal laminations of $\mathbb{R}^3$. These two…
A theorem that is of aid in computing the domain of the adjoint operator is provided. It may serve e.g. as a criterion for selfadjointness of a symmetric operator, for normality of a formally normal operator or for $H$--selfadjointness of…
Two of the most useful tools in topological combinatorics are the nerve lemma and discrete Morse theory. In this note we introduce a theorem that interpolates between them and allows decompositions of complexes into non-contractible pieces…
We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.
We provide a new short proof for the Birman--Solomyak theorem for Hilbert--Schmidt operators and give an application to a Schr\"odinger--Poisson system.
In this note we solve, except for extremely pathological cases, a question posed by Puglisi and Seoane-Sepulveda on the lineability of the set of bounded non-absolutely summing linear operators. We also show how the idea of the proof can be…
The purpose of the present paper is to give an effective version of the noncritical $p$-tame Belyi theorem. That is to say, we compute explicitly an upper bound of the minimal degree of tamely ramified Belyi maps in positive characteristic…