Related papers: Anti-self-dual bihermitian structures on Inoue sur…

In this paper, we show that there are non-properly embedded minimal surfaces with finite topology in a simply connected Riemannian 3-manifold with nonpositive curvature. We show this result by constructing a non-properly embedded minimal…

We give a classification of toric anti-self-dual conformal structures on compact 4-orbifolds with positive Euler characteristic. Our proof is twistor theoretic: the interaction between the complex torus orbits in the twistor space and the…

We prove, assuming the generalized Riemann hypothesis, the Andre-Oort conjecture for Hilbert modular surfaces. More precisely, let K be a real quadratic field and let S be the coarse moduli space of complex abelian surfaces with…

We show that the standard method for constructing closed hyperbolic manifolds of arbitrary dimension possessing reflective symmetries typically produces reflections whose fixed point sets are nonseparating.

We investigate ortho-integral (OI) hyperbolic surfaces with totally geodesic boundaries, defined by the property that every orthogeodesic (i.e. a geodesic arc meeting the boundary perpendicularly at both endpoints) has an integer…

We prove that, both in the hyperbolic and spherical 3-spaces, there exist nonconvex compact boundary-free polyhedral surfaces without selfintersections which admit nontrivial continuous deformations preserving all dihedral angles and study…

We present the construction of Inoue surfaces of type $S^{(+)}/S^{(-)}$ in terms of data arising from real quadratic number fields. We then describe the automorphism group of such surfaces in terms of this data.

In this paper, we study Bertrand surface offsets by considering the dual geodesic trihedron(dual Darboux frame) of the ruled surfaces. We obtain the relationships between the invariants of Bertrand trajectory ruled surfaces. Furthermore, we…

We construct the normal forms of null-K\"ahler metrics: pseudo-Riemannian metrics admitting a compatible parallel nilpotent endomorphism of the tangent bundle. Such metrics are examples of non-Riemannian holonomy reduction, and (in the…

We prove prove a bridge principle at infinity for area-minimizing surfaces in the hyperbolic space $\mathbb{H}^3$, and we use it to prove that any open, connected, orientable surface can be properly embedded in $\mathbb{H}^3$ as an…

For compact Riemannian manifolds with convex boundary, B.White proved the following alternative: Either there is an isoperimetric inequality for minimal hypersurfaces or there exists a closed minimal hypersurface, possibly with a small…

We finish proving that an irreducible automorphism f of a handlebody is efficient if, and only if, a certain standard pair of dual f--invariant laminations have the geometric tightness property. In a previous paper it was proved that this…

We classify hyperbolic polynomials in two real variables that admit a transitive action on some component of their hyperbolic level sets. Such surfaces are called special homogeneous surfaces, and they are equipped with a natural Riemannian…

We reconsider non-degenerate second order superintegrable systems in dimension two as geometric structures on conformal surfaces. This extends a formalism developed by the authors, initially introduced for (pseudo-)Riemannian manifolds of…

A polygonal surface in the pseudo-hyperbolic space H^(2,n) is a complete maximal surface bounded by a lightlike polygon in the Einstein universe Ein^(1,n) with finitely many vertices. In this article, we give several characterizations of…

We show that any weakly partially hyperbolic diffeomorphism on the 2-torus may be realized as the dynamics on a center-stable or center-unstable torus of a 3-dimensional strongly partially hyperbolic system. We also construct examples of…

We prove a surface embedding theorem for 4-manifolds with good fundamental group in the presence of dual spheres, with no restriction on the normal bundles. The new obstruction is a Kervaire-Milnor invariant for surfaces and we give a…

Let $X$ be a compact Hermitian surface, and $g$ be any fixed Gauduchon metric on $X$. Let $E$ be an Hermitian holomorphic vector bundle over $X$. On the bundle $E$, Donaldson's heat flow is gauge equivalent to a flow of holomorphic…

The infinite U Hubbard model, with exclusion of double occupancy of sites, can be considered as a free orthofermion Hamiltonian which is exactly soluble. It is found that the orthofermion distribution function is similar to the mean number…

We give geometric conditions that are necessary and sufficient for the existence of Sinai-Ruelle-Bowen (SRB) measures for $C^{1+\alpha}$ surface diffeomorphisms, thus proving a version of the Viana conjecture. As part of our argument we…