相关论文: Flux Compactifications Grow Lumps

We develop a compactness theory for super Ricci flows, which lays the foundations for the partial regularity theory in [Bam20b]. Our results imply that any sequence of super Ricci flows of the same dimension that is pointed in an…

We analyze the finite-time blow-up of solutions of the heat flow for $k$-corotational maps $\mathbb R^d\to S^d$. For each dimension $d>2+k(2+2\sqrt{2})$ we construct a countable family of blow-up solutions via a method of matched…

We present an alternative "encapsulated" formulation of the Selective Frequency Damping method for finding unstable equilibria of dynamical systems, which is particularly useful when analysing the stability of fluid flows. The formulation…

We use a mix of field theoretic and holographic techniques to elucidate various properties of quantum entanglement entropy. In (3+1)-dimensional conformal field theory we study the divergent terms in the entropy when the entangling surface…

We are concerned with the minimal entropy conditions for one-dimensional scalar conservation laws with general convex flux functions. For such scalar conservation laws, we prove that a single entropy-entropy flux pair $(\eta(u),q(u))$ with…

We introduce and study a conformal heat flow of harmonic maps defined by an evolution equation for a pair consisting of a map and a conformal factor of metric on the two-dimensional domain. This flow is designed to postpone finite time…

High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes address this instability by ensuring that physically relevant…

I study the spontaneous breakdown of supersymmetry when higher-dimensional Yang-Mills or the type-I $SO(32)$ string theory are compactified on magnetized tori. Because of the universal gyromagnetic ratio $g=2$, the splittings of all…

In this paper, we study the prescribed $Q$-curvature problem on closed four-dimensional Riemannian manifolds when the total integral of the $Q$-curvature is a positive integer multiple of the one of the four-dimensional round sphere. This…

This paper concerns the structural stability of smooth cylindrically symmetric transonic flows in a concentric cylinder. Both cylindrical and axi-symmetric perturbations are considered. The governing system here is of mixed…

Using the method of simple current extensions, asymmetric Gepner models of Type IIB with N=1 space-time supersymmetry are constructed. The combinatorics of the massless vector fields suggests that these classical Minkowski string vacua…

The problem for two-dimensional steady water waves with vorticity is considered. Using methods of spatial dynamics, we reduce the problem to a finite dimensional Hamiltonian system. As an application, we prove the existence of non-symmetric…

This article deals with topological assumptions under which the minimal volume entropy of a closed manifold $M$, and more generally of a finite simplicial complex $X$, vanishes or is positive. These topological conditions are expressed in…

We study closed, embedded hypersurfaces in Euclidean space evolving by fully nonlinear curvature flows, whose speed is given by a symmetric, monotone increasing, $1$-homogeneous, positive underlying speed function $F$ composed with a…

This note on the flux homomorphism for strictly contact isotopies complements the recent paper [MS11a] by P. Spaeth and the author. We determine the volume flux restricted to symplectic and volume-preserving contact isotopies and their…

Spontaneous breaking of symmetries leads to universal phenomena. We extend this notion to $(-1)$-form U(1) symmetries. The spontaneous breaking is diagnosed by a dependence of the vacuum energy on a constant background field $\theta$, which…

In this paper, employing a new inequality, we show that under certain curvature pinching condition, the strictly convex closed smooth self-similar solution of $\sigma_k^{\alpha}$-flow must be a round sphere. We also obtain a similar result…

We establish a weak compactness theorem for the moduli space of closed Ricci flows with uniformly bounded entropy, each equipped with a natural spacetime distance, under pointed Gromov-Hausdorff convergence. Furthermore, we develop a…

An old and apparently persistent problem in numerical lattice QCD is that the simulations tend to get trapped in a sector of fixed topological charge when the lattice spacing is taken to zero. The effect sets in very rapidly and may…

Spherical accretion flows are simple enough for analytical study, by solution of the corresponding fluid dynamic equations. The solutions of stationary spherical flow are due to Bondi. The questions of the choice of a physical solution and…