Now showing items 1-20 of 27

    • A circle quotient of a $G_2$ cone 

      Acharya, Bobby Samir; Bryant, Robert L; Salamon, Simon
      A study is made of $R^6$ as a singular quotient of the conical space $R^+\times CP^3$ with holonomy $G_2$ with respect to an obvious action by $U(1)$ on $CP^3$ with fixed points. Closed expressions are found for the induced ...
    • Complex monopoles I: The Haydys monopole equation 

      Nagy, Ákos; 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, Ákos; 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, M; 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; Grossman, Daniel
      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 ...
    • Flat metrics with a prescribed derived coframing 

      Bryant, RL; Clelland, JN
      The following problem is addressed: A $3$-manifold $M$ is endowed with a triple $\Omega = (\Omega^1,\Omega^2,\Omega^3)$ of closed $2$-forms. One wants to construct a coframing $\omega= (\omega^1,\omega^2,\omega^3)$ of $M$ ...
    • From vortices to instantons on the Euclidean Schwarzschild manifold 

      Nagy, Ákos; Oliveira, Gonçalo (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, RL; 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, ...
    • Harmonic Forms, Price Inequalities, and Benjamini-Schramm Convergence 

      Cerbo, Luca F Di; Stern, Mark
      We study Betti numbers of sequences of Riemannian manifolds which Benjamini-Schramm converge to their universal covers. Using the Price inequalities we developed elsewhere, we derive two distinct convergence results. First, ...
    • 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, R; 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 L
      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 ...
    • Manifold Approximation by Moving Least-Squares Projection (MMLS) 

      Sober, B; Levin, D
      In order to avoid the curse of dimensionality, frequently encountered in Big Data analysis, there was a vast development in the field of linear and nonlinear dimension reduction techniques in recent years. These ...
    • New G<inf>2</inf>-holonomy cones and exotic nearly Kahler structures on S6 and S3 x S3 

      Foscolo, L; Haskins, M (Annals of Mathematics, 2017-01-01)
      © 2017 Department of Mathematics, Princeton University. There is a rich theory of so-called (strict) nearly Kahler manifolds, almost-Hermitian manifolds generalising the famous almost complex structure on the 6-sphere induced ...
    • Nonlinear Harmonic Forms and an Indefinite Bochner Formula 

      Stern, Mark (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, RL (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 ...
    • Notes on Projective, Contact, and Null Curves 

      Bryant, Robert L
      These are notes on some algebraic geometry of complex projective curves, together with an application to studying the contact curves in CP^3 and the null curves in the complex quadric Q^3 in CP^4, related by the well-known ...
    • On the conformal volume of 2-tori 

      Bryant, RL (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, RL (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, Luca F Di; Stern, Mark (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 ...