Related papers: Totally Real Minimal Tori in $CP^2$

This article is the continuation of the first named author work "On maximal totally real embeddings". For real analytic compact manifolds equipped with a covariant derivative operator acting on the real analytic sections of its tangent…

We characterize the perimeter-minimizing double bubbles on all flat two-tori and, as corollaries, on the flat infinite cylinder and the flat infinite strip with free boundary. Specifically, we show that there are five distinct types of…

We study topological groups having all closed subgroups (totally) minimal and we call such groups c-(totally) minimal. We show that a locally compact c-minimal connected group is compact. Using a well-known theorem of Hall and Kulatilaka…

We characterize the number of points for which there exist non-empty Terracini sets of points in $\mathbb{P}^n$. Then we study minimally Terracini finite sets of points in $\mathbb{P}^n$ and we obtain a complete description in the case of…

The article proves the Infinitesimal Torelli theorem for surfaces subject to the following conditions: 1) the canonical bundle of a surface is ample and generated by its global sections, 2)the geometric genus $p_g \geq 4$, 3) the…

We prove that every complete, minimally immersed submanifold $f\: M^n \to \mathbb{S}^{n+p}$ whose second fundamental form satisfies $|A|^2 \le np/(2p-1)$, is either totally geodesic, or (a covering of) a Clifford torus or a Veronese surface…

We show optimal FPT-approximability results for solving almost satisfiable systems of modular linear equations, completing the picture of the parameterized complexity and FPT-approximability landscape for the Min-$r$-Lin$(\mathbb{Z}_m)$…

We prove a conjecture about the minimal nonnegative solutions of algebraic Riccati equations associated with reducible singular M-matrices. The result enhances our understanding of the behaviour of doubling algorithms for finding the…

We study entire minimizers of the Allen-Cahn systems. The specific feature of our systems are potentials having a finite number of global minima, with sub-quadratic behaviour locally near their minima. The corresponding formal…

In this note we prove that any minimal $2$-torus in $S^4$ has Morse index at least $6$, with equality if and only if it is congruent to the Clifford torus in some great $S^3\subset S^4$.For a minimal $2$-torus in $S^n$ with vanishing Hopf…

We prove the infinitesimal Torelli theorem for general minimal complex surfaces X's with the first Chern number 3, the geometric genus 1, and the irregularity 0 which have non-trivial 3-torsion divisors. We also show that the coarse moduli…

We give an effective infinitesimal Torelli theorem for cyclic covers of G/P, where G is a simple algebraic group and P is a maximal parabolic subgroup.

Let R be a commutative Noetherian ring. Licci ideals are the ideals of R that can be linked in a finite number of steps to a complete intersection. Each licci ideal admits a rigid deformation, and two licci ideals are in the same Herzog…

We establish a Mittag-Leffler-type theorem with approximation and interpolation for meromorphic curves $M\to \mathbb{C}^n$ ($n\geq 3$) directed by Oka cones in $\mathbb{C}^n$ on any open Riemann surface $M$. We derive a result of the same…

Let $A=\{{\bf a}_1,...,{\bf a}_m\} \subset \mathbb{Z}^n$ be a vector configuration and $I_A \subset K[x_1,...,x_m]$ its corresponding toric ideal. The paper consists of two parts. In the first part we completely determine the number of…

Using discretized orthogonal systems (curvature line systems) with periodicity, created using Darboux transformations and their permutability, we have discrete and semi-discrete k-dimensional isothermic tori which are full in n-dimensional…

In this paper we study the extension of Morita equivalence of noncommutative tori to the supersymmetric case. The structure of the symmetry group yielding Morita equivalence appears to be intact but its parameter field becomes…

We attempt a direct derivation of a conformal field theory description of 2D quantum gravity~+~matter from the formalism of integrable hierarchies subjected to Virasoro constraints. The construction is based on a generalization of the…

In this paper, we investigate the existence of KAM tori for an infinite dimensional Hamiltonian system with finite number of zero normal frequencies. By constructing a constant quantity we show that, for "most" frequencies in the sense of…

We prove that the finite generation of adjoint rings proved in [Cascini and Lazi\'c] implies all the foundational results of the Minimal Model Program: the Rationality, Cone and Contraction theorems, the existence of flips, and termination…