Related papers: Counterexamples of the Geometrization Conjecture

It is well known that the Eisenbud-Goto regularity conjecture is true for arithmetically Cohen-Macaulay varieties, projective curves, smooth surfaces, smooth threefolds in $\mathbb{P}^5$, and toric varieties of codimension two. After J.…

This paper gives an algebraic conjecture which is shown to be equivalent to Thurston's Geometrization Conjecture for closed, orientable 3-manifolds. It generalizes the Stallings-Jaco theorem which established a similar result for the…

We provide a counterexample to the Lagrangian Poincar\'e recurrence conjecture of Ginzburg and Viterbo in all dimensions $6$ and greater.

In this short note we give counterexamples to several results related to extension theorems published recently.

In this paper we adopt a geometric point of view regarding a famous conjecture due to Littlewood in diophantine approximation of real numbers. Following the spirit of the geometric theory of continued fractions, we give a sufficient…

In this short note we give an interpretation of the Kirchheim-Magnani counterexample to metric differentiability in terms of dilatation structures.

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

Two conjectures recently proposed by one of the authors are disproved

This article is an overview of the geometrization conjecture for the local Langlands correspondence formulated by the author.

We construct a counterexample to a conjectured inequality L<2D, relating the diameter D and the least length L of a nontrivial closed geodesic, for a Riemannian metric on the 2-sphere. The construction relies on Guillemin's theorem…

In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.

We prove a conjecture by De Giorgi on the elliptic regularization of semilinear wave equations in the finite-time case.

The bounded orbit conjecture says that every homeomorphism on the plane with each of its orbits being bounded must have a fixed point. Brouwer's translation theorem asserts that the conjecture is true for orientation preserving…

At a first glance, the problem of illuminating the boundary of a convex body by external light sources and the problem of covering a convex body by its smaller positive homothetic copies appear to be quite different. They are in fact two…

By considering suitable axially symmetric slices on the Kruskal spacetime, we construct counterexamples to a recent version of the Penrose inequality in terms of so-called generalized apparent horizons.

We introduce a notion of probabilistic convexity and generalize some classical globalization theorems in Alexandrov geometry. A weighted Alexandrov's lemma is developed as a basic tool.

Five geometrical eqivalents of Goldbach conjecture are given, calling one of them Fermat Like Theorem.

We improve the algebraic methods of Abhyankar for the Jacobian Conjecture in dimension two and describe the shape of possible counterexamples. We give an elementary proof of the result of Heitmann, which states that gcd(deg(P),deg(Q)) is…

We prove existence and uniqueness of solutions for an entropic version of the semi-geostrophic equations. We also establish convergence to a weak solution of the semi-geostrophic equations as the entropic parameter vanishes. Convergence is…

We introduce elliptic hypertoric varieties, which is an elliptic analogue of hypertoric varieties and multiplicative hypertoric varieties. We also prove an elliptic version of Hikita conjecture, which relates elliptic (resp. additive and…