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We use the framework of Quot schemes to give a novel description of the moduli spaces of stable n-pairs, also interpreted as gauged vortices on a closed Riemann surface  with target Matr×n(C), where ...
We consider dimensional reduction of the Bagger-Lambert-Gustavsson theory to a zero-dimensional 3-Lie algebra model and construct various stable solutions corresponding to quantized Nambu-Poisson mani...
We explore a new simple N = 2 SQM model describing the motion over complex manifolds in external gauge fields. The nilpotent supercharge Q of the model can be interpreted as a (twisted) exterior holom...
Given (M, g0) we consider the problem −"2g0+hu + u = (u+)p−1 with (", h) ∈ (0, ¯") × B. Here B is a ball centered at 0 with radius  in the Banach space of all Ck symmetric covaria...
We prove a neighbourhood theorem for arbitrary knots in contact 3-manifolds. As an application we show that two topologically isotopic Legendrian knots in a contact 3-manifold become Legendrian isotop...
We consider the problem −"2gu+u = |u|p−2u in M, where (M, g) is a symmetric Riemannian manifold. We give a multiplicity result for antisymmetric changing sign solutions.
Let (M, g) be a smooth connected compact Riemannian manifold of finite dimension n ≥ 2 with a smooth boundary @M. We consider the problem −"2gu + u = |u|p−2u, u > 0 on M, @u @= 0 on @M w...
Regular infinitesimal flag structures are geometric structures, which occur as underlying structures of parabolic geometries. Among these structures we have for instance conformal structures, contact ...
According to Giroux, contact manifolds can be described as open books whose pages are Stein manifolds. For 5-dimensional contact manifolds the pages are Stein surfaces, which permit a description via ...
This article is concerned with conformal harmonic maps f :  ! M,where  is a closed Riemann surface and M is a compact Riemannian manifold of dimension at least four. We show that when the ambient ma...
In this article we extend the computational geometric curve reconstruction approach to curves in Riemannian manifolds.We prove that the minimal spanning tree, given a sufficiently dense sample set of ...
In this article, we focus on the invariance property of Morse homology on noncompact manifolds. We expect to apply outcomes of this article to several types of Floer homology, thus we define Morse hom...
Kawakubo and Uchida showed that, if a closed oriented 4k-dimensional manifold M admits a semi-free circle action such that the dimension of the fixed point set is less than 2k,then the signature of M ...
In this paper we consider critical points of the following nonlocal energy Ln(u) = Z IRn |(−)n/4u(x)|2dx , (1) where u: Hn/2(IRn) → N N ⊂ IRm is a compact k dimensional smooth manifold w...
The aim of this paper is to extend the Morse theory for geodesics to the conical manifolds. In a previous paper [15] we de ned these manifolds as submanifolds of Rn with a nite number of conical sing...

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