Let (M, g) be a complete noncompact Riemannian manifold. In this paper, we derive a local gradient estimate for positive solutions to a simple nonlinear parabolic equation ∂u ∂t = ∆u+ au log u+ bu on M × [0,+∞), where a, b are two real constants. This equation is closely related to the gradient Ricci soliton. We extend the result of L. Ma (Journal of Functional Analysis 241 (2006) 374-382).

In the framework of three dimensional extended supergravity theories, we demonstrate that there exist non-trivial Killing spinors over BPS soliton configurations, even when the space-time is asymptotically conical. We also show that there are no physical fermionic zero modes on these backgrounds. We further generalize these results to the case of semilocal systems. The connection between Bogomo...

B List has recently studied a geometric flow whose fixed points correspond to static Ricci flat spacetimes. It is now known that this flow is in fact Ricci flow modulo pullback by a certain diffeomorphism. We use this observation to associate to each static Ricci flat spacetime a local Ricci soliton in one higher dimension. As well, solutions of Euclidean-signature Einstein gravity coupled to a...

We construct the world-volume action of a probe D3-brane in AdS5×S with N units of flux. It has the field content, symmetries, and dualities of the U(1) factor of N = 4 U(N + 1) super Yang–Mills theory, spontaneously broken to U(N)×U(1) by being on the Coulomb branch, with the massive fields integrated out. This motivates the conjecture that it is the exact effective action, called a highly eff...

The tachyon field of p-adic string theory is made noncommutative by replacing ordinary products with noncommutative products in its exact effective action. The same is done for the boundary string field theory, treated as the p → 1 limit of the p-adic string. Solitonic lumps corresponding to D-branes are obtained for all values of the noncommutative parameter θ. This is in contrast to usual sca...

Recent development of string theory has shown that noncommutative (NC) models can arise in certain limits of String Theory [1]. Moreover the String Field Theory [2], which is the theory of second quantised string, is based on noncommutative geometry too. Due to their proximity to String Theory noncommutative theories have many features in common with it. It is worthwhile to mention the IR/UV mi...

In the framework of three dimensional extended supergravity theories, we demonstrate that there exist non-trivial Killing spinors over BPS soliton configurations, even when the space-time is asymptotically conical. We also show that there are no physical fermionic zero modes on these backgrounds. We further generalize these results to the case of semilocal systems. The connection between Bogomo...

In this note, we obtain a sharp volume estimate for complete gradient Ricci solitons with scalar curvature bounded below by a positive constant. Using Chen-Yokota’s argument we obtain a local lower bound estimate of the scalar curvature for the Ricci flow on complete manifolds. Consequently, one has a sharp estimate of the scalar curvature for expanding Ricci solitons; we also provide a direct ...

Over the last two decades, extended objects in field theories called solitons have played an important role in particle physics and astrophysics. In certain cases, these solitons possess a conserved topological charge, which guarantees their stability. There are other extended field configurations, however, which are not topological; these “nontopological solitons” are stable for dynamical reas...

Lint ∼ g ψ̄B′ φψB , (1.1) where B′ is the resonance that decays into baryon B and meson φ and g is a coupling constant. It is crucial that this interaction Lagrangian is linear in the meson field. If φ is a pseudoscalar meson this interaction yields the decay width Γ (B′ → Bφ) ∝ g2|~ pφ|, with ~pφ being the momentum of the outgoing meson. The situation is significantly different in soliton model...