arXiv research

We prove the global existence of Dirac-wave maps with curvature term with small initial data on globally hyperbolic manifolds of arbitrary dimension which satisfy a suitable growth condition. In addition, we also prove a global existence result for wave maps under similar assumptions.

In this note a proof is given for global existence and uniqueness of minimal surfaces of Lorentzian type from a cylinder into globally hyperbolic Lorentzian manifolds for given initial values up to the first derivatives.

Smooth convergence shown for curve diffusion flows.

Global obstructions found for conformally Einstein metrics in 6D.

Global solutions and smoothing effects for reaction-diffusion equations on manifolds.

We show that the definition of global hyperbolicity in terms of the compactness of the causal diamonds and non-total imprisonment can be extended to spacetimes with continuous metrics, while retaining all of the equivalences to other notions of global hyperbolicity. In fact, global hyperbolicity is equivalent to the co…

Study describes global existence and convergence of flows on surfaces and fibrations.

We show global existence and convergence results for the pluriclosed flow on manifolds for which certain naturally associated tensor bundles are globally generated.

Proves global existence and uniqueness of solutions for Einstein-scalar-field equations.

We provide sufficient conditions for the existence of a global diffeomorphism between tame Fréchet spaces. We prove a version of the Mountain Pass Theorem which is a key ingredient in the proof of the main theorem.

We present an equivalent criterion for the global existence of Euler's multiplier for an integrable one-form taking into account the corresponding codim-1-foliation. In particular, the impact of inseparable leaves is considered. Here, we suppose that the foliation can be reduced to a graph; we also discuss obstructions…

Global existence and convergence of heat flow for p-harmonic maps.

We prove the existence of global minimizers of Allen-Cahn equation in dimensions $8$ and above. More precisely, given any strictly area-minimizing Lawson's cones, there are global minimizers whose nodal sets are asymptotic to the cones. As a consequence of Jerison-Monneau's program we establish the existence of many co…

We show global existence theorems for Gowdy symmetric spacetimes with type IIB stringy matter. The areal and constant mean curvature time coordinates are used. Before coming to that, it is shown that a wave map describes the evolution of this system.

In this article, existence results concerning temporal functions with additional properties on a globally hyperbolic manifold are obtained. These properties are certain bounds on geometric quantities as lapse and shift. The results are linked to completeness properties and the existence of closed isometric embeddings i…

Generalizes global hyperbolicity to higher signatures and proves compactness.

We introduce the gradient flow of the Seiberg-Witten functional on a compact, orientable Riemannian 4-manifold and show the global existence of a unique smooth solution to the flow. The flow converges uniquely in $C^\infty$ up to gauge to a critical point of the Seiberg-Witten functional.

Global existence of Willmore flow with boundary via Li-Yau inequality.

Example shows no global coordinates on 2-torus's cover.

The paper proves weaker conditions for global smoothings of special Lagrangian submanifolds with conical singularities.

Convex curves evolve into circles over time.

We develop the global moduli theory of symplectic varieties in the sense of Beauville. We prove a number of analogs of classical results from the smooth case, including a global Torelli theorem. In particular, this yields a new proof of Verbitsky's global Torelli theorem in the smooth case (assuming $b_2\geq 5$) which …

The paper studies the Heath-Jarrow-Morton-Musiela equation of the bond market. The equation is analyzed in weighted spaces of functions defined on $[0,+\infty)$. Sufficient conditions for local and global existence are obtained . For equation with the linear diffusion term the conditions for global existence are close …

Global existence and convergence proved for Kazdan-Warner equation with non-negative prescribed function.

Global existence and geometry of constant mass aspect function foliation in perturbed Schwarzschild spacetime studied.

Study proves existence of global solutions for Standard Model on expanding spacetimes.

Given a globally hyperbolic spacetime $M$, we show the existence of a {\em smooth spacelike} Cauchy hypersurface $S$ and, thus, a global diffeomorphism between $M$ and $\R \times S$.

For nearly every major stock market there exist equity and implied volatility indices. These play important roles within finance: be it as a benchmark, a measure of general uncertainty or a way of investing or hedging. It is well known in the academic literature, that correlations and higher moments between different i…

The Klein-Grifone approach to global Finsler geometry is adopted. A global existence and uniqueness theorem for Chern connection is formulated and proved. The torsion and curvature tensors of Chern connection are derived. Some properties and the Bianchi identities for this connection are investigated. A concise compari…

We show that every source connected Lie groupoid always has global bisections through any given point. This bisection can be chosen to be the multiplication of some exponentials as close as possible to a prescribed curve. The existence of bisections through more than one prescribed points is also discussed. We give som…

Some results on existence of global Chebyshev coordinates on a Riemannian manifold or, more generally, on Aleksandrov surface are proved. For instance, if the positive and the negative parts of integral curvature of a Riemannian manifold M are less than 2πeach, then there exist global Chebyshev coordinates on M. These …

Study proves existence of a specific type of flow in geometry.

Study global solutions for Boussinesq systems on curved manifolds.

Global implicit function theorem for Fréchet spaces, solving derivative loss problems.

We give a direct global proof for the existence of symplectic realizations of arbitrary Poisson manifolds.

Global Chern currents and Baum Bott currents defined on arbitrary complex manifolds.

ProGO optimizes non-convex functions without gradients, outperforming existing methods.

Proves existence and uniqueness of solutions for A_n tt*-Toda equations.

Proposes a differentially private bandit algorithm reducing noise over time.

The paper studies minimal surface flow and translating solitons, proving global solutions and convergence.

Paper proves a quantitative estimate for transforming almost complex structures into standard ones.

Study finds conditions for global minimizers on curved manifolds with fast diffusion and nonlocal interactions.

The paper studies global Yamabe flow on AF manifolds, preserving ADM mass.

Chernov-Nemirovski observed that the existence of a globally hyperbolic Lorentzian metric on a (3 + 1)-spacetime pins down a smooth structure on the underlying 4-manifold. In this paper, we point out that the diffeomorphism type of a globally hyperbolic (n + 1)-spacetime is determined by the h-cobordism class of its Ca…

Study explores embedding signature-changing manifolds into higher-dimensional spaces.

Improves global counterfactual explanations for model recourse.

Adopting the pullback approach to global Finsler geometry, the aim of the present paper is to provide intrinsic (coordinate-free) proofs of the existence and uniqueness theorems for the Chern (Rund) and Hashiguchi connections on a Finsler manifold. To accomplish this, we introduce and investigate the notions of semispr…

Global fixed income returns span across multiple maturities and economies, that is, they naturally reside on multi-dimensional data structures referred to as tensors. In contrast to standard "flat-view" multivariate models that are agnostic to data structure and only describe linear pairwise relationships, we introduce…