Related papers: Miyanishi's characterization of the affine 3-space…
Congruences, or $2$-parameter families of lines in $3$-space are of interest in many situations, in particular in geometric optics. In this paper we consider elements of their geometry which are invariant under affine changes of…
If $X$ is a quasi-projective variety over a field $k$ and $\phi$ a birational endomorphism of $X$ that is injective outside a closed subset of codimension $\geq 2$, we prove that $\phi$ is an automorphism. This generalizes an old theorem of…
We show an example of non-simply connected non-liftable Calabi-Yau threefold over an algebraically closed field of characteristic $3$. It is constructed from a simply connected example by S.~Schr\"oer.
A consistent set of asymptotic conditions for higher spin gravity in three dimensions is proposed in the case of vanishing cosmological constant. The asymptotic symmetries are found to be spanned by a higher spin extension of the BMS3…
A classical theorem of Hutchinson asserts that if an iterated function system acts on $\mathbb{R}^d$ by similitudes and satisfies the open set condition then it admits a unique self-similar measure with Hausdorff dimension equal to the…
We complete the classification of algebraic monoid structures on the affine 3-space. The result is based on a reduction of the general case to that of commutative monoids. We also study various algebraic properties of all monoids appearing…
In this note the authors have raised the question regarding the validity of the main result in [1] by setting an example.
Variationality of the equation of conformal geodesics is an important problem in geometry with applications to general relativity. Recently it was proven that, in three dimensions, this system of equations for un-parametrized curves is the…
We prove a no-dimensional Helly theorem for affine spaces and convex sets using the unboundedness framework of Aronov, Goodman, and Pollack (Computational Geometry, 2002). This generalizes the fundamental result of Adiprasito, B\'ar\'any,…
In dimension $n>3$ we show the existence of a compactly supported potential in the differentiability class $C^\alpha$, $\alpha < \frac{n-3}2$, for which the solutions to the linear Schr\"odinger equation in $\R^n$, $$ -i\partial_t u = -…
This paper shows that, in dimensions two or more, there are no holomorphic isometries between Teichm\"uller spaces and bounded symmetric domains in their intrinsic Kobayashi metrics.
The title theorem is proved by example: an algebra of binary relations, closed under intersection and composition, that is not isomorphic to any such algebra on a finite set.
We discuss a formalism where a universe is identified with the support of a wave function propagating through space-time. As opposed to classical cosmology, the resulting universe is not a spacelike section of some space-time, but a…
We provide infinitely many examples of pairs of diffeomorphic, non simply connected K\" ahler manifolds of complex dimension three with different Kodaira dimensions. Also, in any possible Kodaira dimension we find infinitely many pairs of…
We contrast analytical results of a variety of growth models involving subdiffusion, thermal noise and quenched disorder with simulations of these models, concluding that the assumed self-affinity property is more an exception than a rule.…
We establish half-space type results for a class of height-dependent weighted minimal surfaces in $\mathbb{R}^3$, namely critical points of a weighted area functional whose weight depends on the height. When the weight has at most quadratic…
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
The proposition 1 is incomplete. In some of the examples D(a,b) may not obey the triangle inequality. The paper is withdrawn for further elaboration.
In this paper, we study the Calabi-Yau conjectures for complete minimal hypersurfaces $\Sigma^{n}\subset \mathbb{R}^{n+1}$ in dimensions $n\ge 3$. These conjectures ask whether a complete minimal hypersurface must be unbounded, and more…
This note concerns tube domains in ${\mathbb C}^2$ with the envelope of holomorphy not equal to the entire space. We construct examples showing that for such domains the sufficient condition for Kobayashi hyperbolicity due to M. Jarnicki…