arXiv research

Unique expanders found with vanishing entropy.

The paper proves uniqueness of a solution in general relativity.

In this paper, we discuss uniqueness and backward uniqueness for mean curvature flow of non-compact manifolds. We use an energy argument to prove two uniqueness theorems for mean curvature flow with possibly unbounded curvatures. These generalize the results by Chen and Yin. Using similar method, we also obtain a uniqu…

The paper explores uniqueness and non-uniqueness of spacetime extensions in general relativity.

Alternative proof for static black hole uniqueness with nonpositive mass.

The study examines uniqueness and non-uniqueness of minimal surfaces in hyperbolic space.

Proves uniqueness of geometric flow in various Riemannian manifolds.

The paper proves uniqueness of evolving graphs by mean curvature flow under specific conditions.

Unique solutions found for wave-like decaying null infinity equations.

We construct an example of a uniquely ergodic measured foliation on a surface such that the associated translation flow on the orientation double cover is minimal but not uniquely ergodic. We then prove a geometric criterion for the horizontal foliation of a quadratic differential to be uniquely ergodic. The second the…

Unique birational structure proven on Inoue surfaces.

Unique extremal Kähler metric found near a divisor.

Proves uniqueness of Ricci flow with scaling invariant estimates.

Study end sum for surfaces and prove uniqueness results.

Study proves existence and uniqueness of ancient flows from cones.

Revisits geometric PDE uniqueness in Riemannian and CR geometry.

Study proves existence of equilibrium in incomplete economies with discontinuous volatility.

The paper assesses conditions for the uniqueness of k-means clustering.

Proves uniqueness of capillary disks in 3D domains.

Euler's elastica with monotone curvature is uniquely minimal.

The purpose of this paper is to prove the uniqueness of conical Kähler-Einstein metrics, under the condition that the twisted $Ding$-functional is proper. This is a generalization of the author's previous work, and we shall first investigate the uniqueness of twisted Kähler-Einstein metrics, and then use these smooth p…

Paper proves unique tangent maps for complex maps into algebraic varieties.

Mean curvature flow evolves isometrically immersed base manifolds $M$ in the direction of their mean curvatures in an ambient manifold $\bar{M}$. If the base manifold $M$ is compact, the short time existence and uniqueness of the mean curvature flow are well-known. For complete isometrically immersed submanifolds of ar…

Paper studies unique interior points and estimates for generalized translating soliton problems.

Study adds investment gains and losses to recursive utility model, proving existence and uniqueness of utility process.

This paper studies several aspects of asymptotically hyperbolic Einstein metrics, mostly on 4-manifolds. We prove boundary regularity (at infinity) for such metrics and establish uniqueness under natural conditions on the boundary data. By examination of explicit black hole metrics, it is shown that neither uniqueness …

Simple uniqueness proof for McKean-Vlasov systems with weak feedback.

Study on portfolio optimization and risk analysis, proving non-uniqueness and suggesting a method to resolve it.

Paper studies Kähler-Ricci flow convergence on Fano manifolds.

Proves local existence and uniqueness of SMCF in Euclidean spaces.

Proves existence and uniqueness of loop equation solutions for semisimple Frobenius manifolds.

We examine the question of uniqueness for the equivariant reduction of the harmonic map heat flow in the energy supercritical dimension. It is shown that, generically, singular data can give rise to two distinct solutions which are both stable, and satisfy the local energy inequality. We also discuss how uniqueness can…

New proof shows solutions to Lichnerowicz equation exist.

Simplified proof of mass center system's uniqueness and generalized Pappus' theorem across Euclidean, spherical, and hyperbolic geometries.

Paper proves uniqueness of specific spacetime surfaces in a lightcone.

The paper proves strong uniqueness and rectifiability of generalized cylindrical singularities in Ricci flow.

The Ricci flow is an evolution system on metrics. For a given metric as initial data, its local existence and uniqueness on compact manifolds was first established by Hamilton \cite{Ha1}. Later on, De Turck \cite{De} gave a simplified proof. In the later of 80's, Shi \cite{Sh1} generalized the local existence result to…

We revisit the problem of uniqueness for the Ricci flow and give a short, direct proof, based on the consideration of a simple energy quantity, of Hamilton/Chen-Zhu's theorem on the uniqueness of complete solutions of uniformly bounded curvature. With a variation of this quantity and technique, we further prove a uniqu…

Paper defines parabolic frequency for Ricci flow solutions, proving monotonicity and uniqueness.

New research proves uniqueness of maximal spacetime boundaries under certain conditions.

Characterizes and analyzes the large scale geometry of big mapping class groups of surfaces.

Unique Calabi-Yau metrics found on C^n.

Study finds unique and non-existent constant mean curvature hypersurfaces in specific spacetimes.

Note on minimal maps' uniqueness via singular values.

Uniqueness theorem for extremal charged black holes in de Sitter space.

In this paper, we obtain a necessary and sufficient condition for $L^{\infty}$-uniqueness of Sturm-Liouville operator $a(x)\frac{d^2}{dx^2} + b(x) \frac d{dx} -V$ on an open interval of $\rr$, which is equivalent to the $L^1$-uniqueness of the associated Fokker-Planck equation. For a general elliptic operator $\LL^V:=Δ…

Uniqueness of 1D bi-Schrödinger flow proven from flat torus to compact space.

Study solves inverse problems for real principal type operators using unique data sets and ray transforms.