arXiv subjects
Publications and source records attributed to Juergen Jost.
We consider solutions of a Toda system for SU(N+1) and show that any solution with finite exponential integral cam be obtained from a rational curve in complex projective space of dimension N
We obtain a Bernstein theorem for special Lagrangian graphs in n-dimensional complex space for arbitrary n only assuming bounded slope, but no quantitative restriction.
We analyze solutions of the Toda system and establish an optimal Moser-Trudinger inequality
The present paper contains an interpretation and generalization of Novikov's theory of Morse type inequalities for 1-forms in terms of Conley's theory for dynamical systems.
We use pluriharmonic maps to study representations of fundamental groups of algebraic manifolds. This approach is functorial in the sense that the restriction of such a map to a fiber of a fibration remains pluriharmonic, and on this basis, we can investigate the relation between the properties of the original representation and what can be inferred by restricting it to the fibers of a fibration.
We report a noise induced delay of bifurcation in a simple pulse-coupled neural circuit. We study the behavior of two neural oscillators, each individually governed by saddle-node dynamics, with reciprocal excitatory synaptic connections. In the deterministic circuit, the synaptic current amplitude acts as a control parameter to move the circuit from a mono-stable regime through a bifurcation into a bistable regime. In this regime stable sustained anti-phase oscillations in both neurons coexist with a stable rest state. We introduce a small amount of random current into both neurons to model possible randomly arriving synaptic inputs. We find that such random noise delays the onset of bistability, even though in decoupled neurons noise tends to advance bifurcations and the circuit has only excitatory coupling. We show that the delay is dependent on the level of noise and suggest that a curious stochastic ``anti-resonance'' is present.
The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection $A$ on a line bundle $L$ and a section $ϕ$ of another bundle $W^+$ constructed from $L$ and a spinor bundle on a given four-dimensional Riemannian manifold. We show the regularity of weak solutions and the Palais-Smale condition for this functional.