arXiv research

Continuous time analysis of bubble formation in harmonic maps.

Study on Yang-Mills heat flow on $\mathbb{R}^4$ bundles, showing infinite time bubbling.

We consider a constructive model for asset price bubbles, where the market price $W$ is endogenously determined by the trading activity on the market and the fundamental price $W^F$ is exogenously given, as in the work of Jarrow, Protter and Roch (2012). To justify $W^F$ from a fundamental point of view, we embed this …

Small bubbles sliding on a boundary maintain half-spherical shape.

In this paper, we show that small spherical soap bubbles in irreducible simply connected symmetric spaces of rank greater than one are constructed from the limits of a certain kind of modified mean curvature flows starting from small spheres in the Euclidean space of dimension equal to the rank of the symmetric space, …

The paper classifies ovals in 4D space for a specific flow.

We define a family of functionals generalizing the Yang-Mills functional. We study the corresponding gradient flows and prove long-time existence and convergence results for subcritical dimensions as well as a bubbling criterion for the critical dimensions. Consequently, we have an alternate proof of the convergence of…

Wave maps can have multiple bubbling solutions at blow-up points.

New heat flow for harmonic maps avoids singularities but not bubbles.

Deep model predicts Bitcoin price movements without retraining.

Study ancient flows in 4D, classifying based on bubble-sheet eigenvalues.

We analyse the asymptotic behaviour of solutions of the Teichmüller harmonic map flow from cylinders, and more generally of `almost minimal cylinders', in situations where the maps satisfy a Plateau-boundary condition for which the three-point condition degenerates. We prove that such a degenerating boundary condition …

Physics-guided deep learning improves CFD for bubbly flow simulations.

Study proves Lojasiewicz inequalities for harmonic maps near simple bubble trees.

The four-dimensional sphere is uniquely rigid in terms of scalar curvature.

Paper evaluates whether AI is a bubble or a productivity revolution.

Researchers found a new type of singularity in surface evolution equations.

We study the risk assessment of uncertain cash flows in terms of dynamic convex risk measures for processes as introduced in Cheridito, Delbaen, and Kupper (2006). These risk measures take into account not only the amounts but also the timing of a cash flow. We discuss their robust representation in terms of suitably p…

New Ricci flows found with Einstein orbifolds at infinity.

We consider the formation of singularities along the Calabi flow with the assumption of the uniform Sobolev constant. In particular, on Kähler surface we show that any "maximal bubble" has to be a scalar flat ALE Kähler metric. In some certain classes on toric Fano surface, the Sobolev constant is a priori bounded alon…

Paper disproves potential singularity models for 3D hypersurfaces in R^4.

In the present paper we study a type of generic singularity of mean curvature flow modelled on the bubble-sheet $\mathbb S^1\times\mathbb R^3$ , and we derive an asymptotic profile for a neighborhood of singularity.

We study the long time behaviour of Ricci flow with bubbling-off on a possibly noncompact $3$-manifold of finite volume whose universal cover has bounded geometry. As an application, we give a Ricci flow proof of Thurston's hyperbolisation theorem for $3$-manifolds with toral boundary that generalizes Perelman's proof …

Harmonic map flow preserves almost-holomorphic maps without singularities.

Study classifies bubbles of Type I singularities in Kähler-Ricci flow on compact surfaces.

In this article, we introduce a mass-decreasing flow for asymptotically flat three-manifolds with nonnegative scalar curvature. This flow is defined by iterating a suitable Ricci flow with surgery and conformal rescalings and has a number of nice properties. In particular, wormholes pinch off and nontrivial spherical s…

Harmonic map flow's singularity properties proven with Lojasiewicz inequalities.

This paper develops Yang-Mills flow on Riemannian manifolds with special holonomy. By analogy with the second-named author's thesis, we find that a supremum bound on a certain curvature component is sufficient to rule out finite-time singularities. Assuming such a bound, we prove that the infinite-time bubbling set is …

We show uniqueness of classical solutions of the normalised two-dimensional Hamilton-Ricci flow on closed, smooth manifolds for smooth data among solutions satisfying (essentially) only a uniform bound for the Liouville energy and a natural space-time $L^2$-bound for the time derivative of the solution. The result is s…

We prove the longtime existence and convergence of the Calabi flow on toric Fano surfaces in a large family of Kahler classes where the class has positive extremal Hamiltonian potential and the initial Calabi energy is bounded by some constant. This is an extension of our previous work. We use the toric condition in a …

Several results on existence and convergence of the Yang-Mills flow in dimension four are given. We show that a singularity modeled on an instanton cannot form within finite time. Given low initial self-dual energy, we then study convergence of the flow at infinite time. If an Uhlenbeck limit is anti-self-dual and has …

The paper proves a Lojasiewicz inequality for maps from the 2-sphere to itself.

Model explains stock price bubbles through debt crises and financial crashes.

We study the evolution of wormhole geometries under Ricci flow using numerical methods. Depending on values of initial data parameters, wormhole throats either pinch off or evolve to a monotonically growing state. The transition between these two behaviors exhibits a from of critical phenomena reminiscent of that obser…

CR Yamabe flow fails to converge on small deformations of the standard CR three-sphere.

Solves complex Hessian equations in unstable cases, proving unique canonical solutions with singularities.

Characterizes critical points in convex double and triple bubbles.

Survey on soap bubble partitions and their stability.

Bubbles are essential in certain economic models with high growth and low interest rates.

Study Yang-Mills connections on four-manifolds, derive obstructions to bubbling.

Rational bubbles form in nonstationary models of real assets.

Existence of double bubbles with high constant mean curvatures in Riemannian manifolds.

Defines speculative bubbles in discrete-time models based on discounted stock price losing mass.

Degenerate solutions found in 2D H-system bubbles with higher degrees.

The Teichmüller harmonic map flow deforms both a map from an oriented closed surface $M$ into an arbitrary closed Riemannian manifold, and a constant curvature metric on $M$, so as to reduce the energy of the map as quickly as possible [16]. The flow then tries to converge to a branched minimal immersion when it can [1…

This is the third installment of the Financial Bubble Experiment. Here we provide the digital fingerprint of an electronic document in which we identify 27 bubbles in 27 different global assets; for 25 of these assets, we present windows of dates of the most likely ending time of each bubble. We will provide that docum…

On 2 November 2009, the Financial Bubble Experiment was launched within the Financial Crisis Observatory (FCO) at ETH Zurich (\url{http://www.er.ethz.ch/fco/}). In that initial report, we diagnosed and announced three bubbles on three different assets. In this latest release of 23 December 2009 in this ongoing experime…

Trading bubbles form when traders adapt to price mismatches.