arXiv research

The Björling problem is explored for Born-Infeld solitons.

Study Born-Infeld solitons and solve Björling problem for them.

We show that a Born-Infeld soliton can be realised either as a spacelike minimal graph or timelike minimal graph over a timelike plane or a combination of both away from singular points. We also obtain some exact solutions of the Born-Infeld equation from already known solutions to the maximal surface equation. Further…

The height function of various surfaces decomposes into finite sums of scaled and translated versions of itself.

In this paper, we discuss a one parameter family of complex Born-Infeld solitons arising from a one parameter family of minimal surfaces. The process enables us to generate a new solution of the B-I equation from a given complex solution of a special type (which are abundant). We illustrate this with many examples. We …

Lie symmetry group method is applied to study the Born-Infeld equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra symmetries is determined.

A new AI optimization method uses energy-conserving dynamics inspired by Born-Infeld theory.

We obtain the Weierstrass-Enneper representation for maximal graphs(whose Gauss map is one-one) in Lorentz-Minkowski space. For this we use the method of Barbishov and Chernikov, which they have used to find the solutions of Born-Infeld equation in hodographic coordinates. We could use their method in our case, because…

The paper studies graphs with prescribed Lorentzian mean curvature and their relation to Born-Infeld theory.

We study a functional that derives from the classical Yang-Mills functional and Born-Infeld theory. We establish its first variation formula and prove the existence of critical points. We also obtain the second variation formula.

We prove long time existence and convergence results for the pluriclosed flow, which imply geometric and topological classification theorems for generalized Kähler structures. Our approach centers on the reduction of pluriclosed flow to a degenerate parabolic equation for a $(1,0)$-form, introduced in \cite{ST2}. We ob…

In this paper we investigate relations between solutions to the minimal surface equation in Euclidean $3$-space $\mathbb{E}^3$, the zero mean curvature equation in Lorentz-Minkowski $3$-space $\mathbb{L}^3$ and the Born-Infeld equation under Wick rotations. We prove that the existence conditions of real solutions and i…

Let $F: [0, \infty) \to [0, \infty)$ be a strictly increasing $C^2$ function with $F(0)=0$. We unify the concepts of $F$-harmonic maps, minimal hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and introduce $F$-Yang-Mills fields, $F$-degree, $F$-lower degree, and generalized Yang-Mills-Born-Infeld…

A large class of variational equations for geometric objects is studied. The results imply conformal monotonicity and Liouville theorems for steady, polytropic, ideal flow, and the regularity of weak solutions to generalized Yang-Mills and Born-Infeld systems.

In this article we consider the motion of relativistic strings in the Minkowski space $\textbf{R}^{1+n}$. Those surfaces are known as a timelike minimal surface, and described by a system with $n$ nonlinear wave equations of Born-Infeld type. By constructing a suitable Nash-Moser iteration scheme, we prove that the $n$…

In this paper we obtain the general solution to the minimal surface equation, namely its local Weierstrass-Enneper representation, by using a system of hodographic coordinates. This is done by using the method of solving the Born-Infeld equations by Whitham. We directly compute conformal coordinates on the minimal surf…

In this paper a convergent series expansion is constructed to solve the prescribed mean curvature equation for n-dimensional hypersurfaces in n+1 dimensional Euclidean or Minkowskian space(time) which are graphs of a smooth real function u, and whose mean curvature function H is not too large in Hoelder norm, and integ…

We study conditions on the topological D-branes of types A and B obtained by requiring a proper matching of the spectral flow operators on the boundary. These conditions ensure space-time supersymmetry and stability of D-branes. In most cases, we reproduce the results of Marino-Minasian-Moore-Strominger, who studied th…

The paper classifies a type of solitons in Euclidean spaces.

Study on shrinking solitons of generalized Ricci flow.

New examples of solitons found as warped products.

We investigate the Penrose limits of classical string and M-theory backgrounds. We prove that the number of (super)symmetries of a supergravity background never decreases in the limit. We classify all the possible Penrose limits of AdS x S spacetimes and of supergravity brane solutions. We also present the Penrose limi…

Study on Yamabe solitons with applications and structure elucidation.

We classify Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups. All algebraic Ricci solitons that we obtain are sol-solitons. In particular, we prove that, contrary to the Riemannian case, Lorentzian Ricci solitons need not to be algebraic Ricci solitons. We classify Algebraic Ricci Solitons of three-d…

The study examines Riemann solitons and almost solitons on specific Kenmotsu manifolds.

Study on $η$-Ricci-Yamabe solitons on Riemannian submersions.

Given a compact Riemannian manifold $(M^n,g)$ and a fixed cohomology class, $[α^*] \in H^k(M)$, we consider the existence of a minimizer $α\in [α^*]$ of the generalized minimal surface energy $\int_M \sqrt{1+|α|^2} dV_g$. When $k = 1$, we prove the existence of unique minimizers for every cohomology class $[α^*]$. Next…

Study on geometric properties of second Ricci solitons.

Study on Ricci-like solitons and gradient solitons on specific manifolds.

The study classifies steady Ricci solitons based on geometric conditions.

Study on p-biharmonic maps from gradient Ricci solitons, focusing on 2D cigar soliton.

The study characterizes spacetimes with specific solitons in $f(\mathcal{R})$-gravity.

We prove some results for the solitons of the Ricci-Bourguignon flow, generalizing corresponding results for Ricci solitons. Taking motivation from Ricci almost solitons, we then introduce the notion of Ricci-Bourguignon $almost$ solitons and prove some results about them which generalize previous results for Ricci alm…

Extends soliton theory to non-compact cases.

Paper shows constant σk-curvature for quasi k-Yamabe solitons.

Researchers study solitons on homogeneous manifolds, proving properties of specific types of solitons.

The paper characterizes Ricci solitons on the Poincaré upper half plane.

Characterizes $*$-$k$-Ricci-Yamabe solitons on Kenmotsu manifolds.

The paper explores almost Ricci solitons on Finsler spaces, proving conditions for their existence.

New families of Ricci solitons found with collapsing volume.

The study classifies h-almost Ricci-Yamabe solitons in various paracontact manifolds.

Study on warped product Yamabe solitons with constant fiber curvature.

Study on para-Sasakian metrics and their solitons.

Study on steady solitons' curvature behavior near infinity.

The study classifies specific types of solitons with bounded scalar curvature.

Unique steady and expanding solitons with spherical links identified.

The paper examines triviality of Ricci-Bourguignon harmonic solitons.

We use the bracket flow/algebraic soliton approach to study the Laplacian flow of $G_2$-structures and its solitons in the homogeneous case. We prove that any homogeneous Laplacian soliton is equivalent to a semi-algebraic soliton (i.e.\ a $G$-invariant $G_2$-structure on a homogeneous space $G/K$ that flows by pull-ba…