Now showing items 1-20 of 21

    • Complex monopoles I: The Haydys monopole equation 

      Nagy, Akos; Oliveira, Gonçalo
      We study complexified Bogomolny monopoles using the complex linear extension of the Hodge star operator, these monopoles can be interpreted as solutions to the Bogomolny equation with a complex gauge group. Alternatively, ...
    • Complex monopoles II: The Kapustin--Witten monopole equation 

      Nagy, Akos; Oliveira, Gonçalo
      We study complexified Bogomolny monopoles in 3 dimensions by complexifying the compact structure groups. In this paper we use the conjugate linear extension of the Hodge star operator which yields a reduction of ...
    • Counting Yang-Mills Dyons with Index Theorems 

      Stern, Mark A; Yi, P (Phys.Rev. D, 2017-06-01)
      We count the supersymmetric bound states of many distinct BPS monopoles in N=4 Yang-Mills theories and in pure N=2 Yang-Mills theories. The novelty here is that we work in generic Coulombic vacua where more than one adjoint ...
    • Exterior Differential Systems and Euler-Lagrange Partial Differential Equations 

      Bryant, Robert; Griffiths, Phillip A; Grossman, DA
      We use methods from exterior differential systems (EDS) to develop a geometric theory of scalar, first-order Lagrangian functionals and their associated Euler-Lagrange PDEs, subject to contact transformations. The first ...
    • From vortices to instantons on the Euclidean Schwarzschild manifold 

      Nagy, Á; Oliveira, G (2018-01-18)
      The first irreducible solution of the $\SU (2)$ self-duality equations on the Euclidean Schwarzschild (ES) manifold was found by Charap and Duff in 1977, only 2 years later than the famous BPST instantons on $\rl^4$ were ...
    • Geodesic behavior for Finsler metrics of constant positive flag curvature on $S^2$ 

      Bryant, Robert; Foulon, P; Ivanov, S; Matveev, VS; Ziller, W (2017-11-01)
      We study non-reversible Finsler metrics with constant flag curvature 1 on S^2 and show that the geodesic flow of every such metric is conjugate to that of one of Katok's examples, which form a 1-parameter family. In particular, ...
    • Irreducible Ginzburg-Landau fields in dimension 2 

      Nagy, Á (2018-01-18)
      Ginzburg--Landau fields are the solutions of the Ginzburg--Landau equations which depend on two positive parameters, $\alpha$ and $\beta$. We give conditions on $\alpha$ and $\beta$ for the existence of irreducible solutions ...
    • Laplacian Flow for Closed $G_2$-Structures: Short Time Behavior 

      Bryant, Robert; Xu, F (2011-01-11)
      We prove short time existence and uniqueness of solutions to the Laplacian flow for closed $G_2$ structures on a compact manifold $M^7$. The result was claimed in \cite{BryantG2}, but its proof has never appeared.
    • Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms 

      Bryant, Robert
      The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is ...
    • Nonlinear Harmonic Forms and an Indefinite Bochner Formula 

      Stern, Mark A (2017-06-01)
      We introduce the study of nonlinear harmonic forms. These are forms which minimize the $L_2$ energy in a cohomology class subject to a nonlinear constraint. In this note, we include only motivations and the most basic existence ...
    • Notes on exterior differential systems 

      Bryant, Robert (2014-05-13)
      These are notes for a very rapid introduction to the basics of exterior differential systems and their connection with what is now known as Lie theory, together with some typical and not-so-typical applications to illustrate ...
    • On the conformal volume of 2-tori 

      Bryant, Robert (2015-07-06)
      This note provides a proof of a 1985 conjecture of Montiel and Ros about the conformal volume of tori. (This material is not really new; I'm making it available now because of requests related to recent interest ...
    • On the convex Pfaff-Darboux Theorem of Ekeland and Nirenberg 

      Bryant, Robert (2015-12-22)
      The classical Pfaff-Darboux Theorem, which provides local `normal forms' for 1-forms on manifolds, has applications in the theory of certain economic models. However, the normal forms needed in these models come with an ...
    • Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points 

      Cerbo, LFD; Stern, Mark A (2017-06-01)
      We derive Price inequalities for harmonic forms on manifolds without conjugate points and with a negative Ricci upper bound. The techniques employed in the proof work particularly well for manifolds of non-positive sectional ...
    • Real hypersurfaces in unimodular complex surfaces 

      Bryant, Robert (2004-07-27)
      A unimodular complex surface is a complex 2-manifold X endowed with a holomorphic volume form. A strictly pseudoconvex real hypersurface M in X inherits not only a CR-structure but a canonical coframing as well. In this ...
    • Recent Advances in the Theory of Holonomy 

      Bryant, Robert
      This article is a report on the status of the problem of classifying the irriducibly acting subgroups of GL(n,R) that can appear as the holonomy of a torsion-free affine connection. In particular, it contains an account ...
    • Remarks on the geometry of almost complex 6-manifolds 

      Bryant, Robert
      This article is mostly a writeup of two talks, the first given in the Besse Seminar at the Ecole Polytechnique in 1998 and the second given at the 2000 International Congress on Differential Geometry in memory of Alfred ...
    • Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces 

      Bryant, Robert (2001-03-05)
      I use local differential geometric techniques to prove that the algebraic cycles in certain extremal homology classes in Hermitian symmetric spaces are either rigid (i.e., deformable only by ambient motions) or quasi-rigid ...
    • S.-S. Chern's study of almost-complex structures on the six-sphere 

      Bryant, Robert (2014-05-14)
      In 2003, S.-s. Chern began a study of almost-complex structures on the 6-sphere, with the idea of exploiting the special properties of its well-known almost-complex structure invariant under the exceptional group $G_2$. ...
    • Second order families of special Lagrangian 3-folds 

      Bryant, Robert
      A second order family of special Lagrangian submanifolds of complex m-space is a family characterized by the satisfaction of a set of pointwise conditions on the second fundamental form. For example, the set of ruled special ...