Investigates conditions for Poincaré map existence and uniqueness in systems with impulse effects.
problem Existence and uniqueness of Poincaré maps for systems with impulse effects.
method Investigates sufficient conditions for the existence and uniqueness of Poincaré maps for dynamical systems with impulse effects evolving on a differentiable manifold.
result Shows sufficient conditions for the existence and uniqueness of Poincaré maps for systems with impulse effects.
The paper proves short-time existence and uniqueness of Ricci flow on Finsler manifolds.
problem Existence and uniqueness of Ricci flow solutions on Finsler manifolds.
method Investigation of short-time existence and uniqueness of Ricci flow solutions on Finsler manifolds.
result Theorems demonstrating the short-time existence of the flow solution for n-dimensional Finsler manifolds and the uniqueness of the solution for isotropic Finsler manifolds.
Study proves existence and uniqueness of Yang-Mills flow on cylindrical 4-manifolds.
problem Existence and uniqueness of Yang-Mills flow on specific 4-manifolds.
method Established through mathematical proofs and hypotheses on underlying data.
result Long-time existence and infinite-time convergence of the Yang-Mills flow.
Study adds investment gains and losses to recursive utility model, proving existence and uniqueness of utility process.
problem Existence and uniqueness of utility process in a recursive utility model with investment gains and losses.
method Generalized recursive utility model with constant elasticity of intertemporal substitution and relative risk aversion degree. Proved existence and uniqueness in a specific, finite-state Markovian setting.
result Utility process exists and is unique when agent derives nonnegative gain-loss utility, and non-existent or non-unique otherwise.
Study on Kähler Ricci flow existence and uniqueness.
problem Existence and uniqueness of Kähler-Einstein metrics.
method Kähler Ricci flow and curvature analysis.
result Existence criteria for Kähler Ricci flow solutions and uniqueness of Kähler-Einstein metrics.
The paper proves uniqueness and existence of pseudohermitian submanifolds in Heisenberg groups.
problem Geometric properties of pseudohermitian submanifolds in Heisenberg groups.
method Study and prove uniqueness and existence theorems.
result Uniqueness and existence theorems for pseudohermitian submanifolds in Heisenberg groups.
Proves existence and uniqueness of solutions to a complex equation with gradient term.
problem Existence and uniqueness of solutions to complex Monge-Ampère equation with gradient term.
method Existence and uniqueness proved using complex Hermitian manifolds.
result Existence and uniqueness of solutions proved.
Paper shows non-uniqueness of solutions to a specific Minkowski problem.
problem Investigating non-uniqueness in the dual Lp-Minkowski problem for p<0<q. method Proved existence of solutions and constructed an example.
result Non-uniqueness of solutions to the dual Lp-Minkowski problem. Let ψ be a given function defined on a Riemannian space. Under what conditions does there exist a compact starshaped hypersurface M for which ψ, when evaluated on M, coincides with the m−th elementary symmetric function of principal curvatures of M for a given m? The corresponding existence and uniqueness…
Simplified proof for Ricci flow on closed Einstein manifolds.
problem Local existence and uniqueness of Ricci flow on closed Einstein manifolds.
method Simple proof using new metric space setting.
result Local existence and uniqueness of Ricci flow proved.
Study proves existence, uniqueness, and stability for specific stochastic Volterra equations.
problem Analyzing existence, uniqueness, and stability of affine stochastic Volterra equations with L1-kernels. method Approximations with L2-kernels, stability result, duality argument, deterministic Riccati--Volterra integral equation. result Established weak uniqueness for the equations using Fourier--Laplace transform and a deterministic Riccati--Volterra integral equation.
The study proves the existence and uniqueness of near-horizon geometries for 5D black holes.
problem Existence and uniqueness of near-horizon geometries for 5-dimensional black holes.
method Proved existence and uniqueness of bi-axisymmetric near-horizon geometries with specific topologies and charges.
result Existence and uniqueness of near-horizon geometries for 5D black holes established up to isometry.
Analyzed Guyon's volatility model for existence and uniqueness.
problem Existence and uniqueness of a strong solution for Guyon's volatility model.
method Proved existence and uniqueness of a strong solution, characterised boundary behavior, derived asymptotic option prices, and small-time estimates.
result Existence and uniqueness of a strong solution for Guyon's volatility model.
Study existence and uniqueness of solutions for Yamabe problem on non-compact manifolds with negative curvature.
problem Existence and uniqueness of solutions for the Yamabe problem on non-compact manifolds of negative curvature type.
method Used partial C2 decay of the metric and local volume ratio condition to establish existence and uniqueness results. result Established existence and uniqueness results for the Yamabe problem on non-compact manifolds of negative curvature type.
New proof shows solutions to Lichnerowicz equation exist.
problem Existence of solutions to the Lichnerowicz equation in general relativity.
method A new proof approach.
result Existence and uniqueness of solutions proven.
Proves existence and uniqueness of mean curvature flow.
problem Existence and uniqueness of mean curvature flow.
method Heat kernel estimates and contraction mapping principle.
result Continuous dependence of mean curvature flow on initial data.
Generalizes CMC-foliation existence and uniqueness to broader hyperbolic manifolds.
problem Existence and uniqueness of constant mean curvature foliations in asymptotically hyperbolic manifolds.
method Generalization of previous results to a broader class of manifolds.
result CMC-foliation characterizes center of mass in the generalized setting.
The paper proves existence and uniqueness of slant immersions in complex space forms.
problem Existence and uniqueness of slant immersions in complex space forms.
method Established existence and uniqueness theorems for pointwise slant immersions of Riemannian manifolds into a complex space form.
result Existence and uniqueness theorems for pointwise slant immersions of Riemannian manifolds into a complex space form.
Study proves existence and uniqueness of ancient flows from cones.
problem Existence and uniqueness of ancient rescaled mean curvature flows.
method Proved existence and uniqueness using strong uniqueness theorem.
result Proved existence and uniqueness of ancient flows from cones.
Study Fu-Yau equation on astheno-Kähler manifolds, proving existence and uniqueness.
problem Existence and uniqueness of solutions to Fu-Yau equation on astheno-Kähler manifolds.
method Analysis of Fu-Yau equation on compact Hermitian manifolds, proving existence and uniqueness for astheno-Kähler manifolds.
result Proved existence and uniqueness of solutions for Fu-Yau equation on astheno-Kähler manifolds.
Proves existence and uniqueness of solutions to the Lp Gaussian Minkowski problem.
problem Existence and uniqueness of solutions to the Lp Gaussian Minkowski problem.
method Analyzes existence and uniqueness of solutions for different values of p.
result Existence and uniqueness of smooth solutions for p > n.
Proves existence and uniqueness of solutions for a specific minimal surface equation.
problem Existence and uniqueness of solutions for a singular minimal surface equation.
method Proves existence and uniqueness of classical solutions for the Dirichlet problem.
result Proves existence and uniqueness of solutions for the α-singular minimal surface equation. Study proves existence of equilibrium in incomplete economies with discontinuous volatility.
problem Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
method Established existence of solution for Markovian quadratic BSDEs with discontinuous generators using unique continuation and backward uniqueness.
result Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
Proves existence and uniqueness of curvature motion for regular networks.
problem Existence and uniqueness of motion by curvature for regular networks.
method Proves existence and uniqueness using $W^{2- rac{2}{p}}_p$ initial data and investigates regularization effects.
result Proves existence and uniqueness of motion by curvature for regular networks.
Proves uniqueness and existence of toric gravitational instantons.
problem Proves uniqueness and existence of four-dimensional asymptotically flat, Ricci-flat, toric gravitational instantons.
method Adapting black hole uniqueness theorems to a harmonic map formulation of Ricci-flat metrics with torus symmetry.
result Proves that instantons are uniquely characterised by their rod structure and that for every admissible rod structure, there exists a smooth instanton.
Paper finds unique maximal hypersurfaces in open spacetimes.
problem Finding unique maximal hypersurfaces in open spacetimes.
method Natural geometric and physical assumptions applied to spatially open Robertson-Walker spacetimes with flat fiber.
result New uniqueness and non-existence results for complete maximal hypersurfaces.
Proves local existence and uniqueness of SMCF in Euclidean spaces.
problem Proving existence and uniqueness of SMCF.
method Local existence and uniqueness proof for SMCF.
result Local existence and uniqueness of SMCF proved.
Proves global existence and uniqueness of solutions for Einstein-scalar-field equations.
problem Global existence and uniqueness of solutions for specific Einstein-scalar-field equations.
method Proves global existence and uniqueness of classical solutions with small initial data and wake-like decaying null infinity.
result Global existence and uniqueness of solutions for the equations with wake-like decaying null infinity.
Local existence and uniqueness of Bakry-Émery Ricci flow solutions on finite graphs.
problem Analyzing the behavior of Ricci flow on finite graphs.
method Local existence and uniqueness proof for solutions of the Bakry-Émery Ricci flow.
result Local existence and uniqueness of solutions to the Ricci flow on finite graphs.
Study on geometric variational problems for existence, regularity, and uniqueness of solutions.
problem Geometric variational problems, focusing on existence, regularity, and uniqueness of solutions.
method Formulated in Federer and Fleming's theory of currents, discussed the existence theory, and presented core ideas of the (interior) regularity theory for area-minimizing currents and optimal transport paths. Two original results on generic uniqueness of solutions were presented.
result Generic uniqueness of solutions for both Plateau's problem and optimal branched transport problem.
Study geodesics in low regularity metrics, proving existence and uniqueness.
problem Existence and uniqueness of geodesics in low regularity metrics.
method Analyzes Riemannian and Lorentzian manifolds with low regularity metrics, proving existence and uniqueness of solutions.
result Generalizes recent results on existence, regularity, and uniqueness of solutions for geodesics in low regularity metrics.
Paper proves uniqueness of special Lagrangian pair in Calabi-Yau 3-fold.
problem Existence and uniqueness of special Lagrangian pair of pants in Calabi-Yau 3-fold.
method Proves uniqueness of a special Lagrangian pair of pants with three asymptotically cylindrical ends.
result No other special Lagrangian pair satisfies the conjecture.
The paper addresses dynamic capital structure models with defaultable debt, proving existence and uniqueness.
problem Dynamic capital structure models with an investor break-even condition may not generate a contraction mapping.
method Provided an example and used a dual problem and change of measure to prove existence and uniqueness.
result A unique Markov-perfect equilibrium exists where firm decisions reflect state-dependent targets.
Unique inhomogeneous ruled hypersurface found in complex hyperbolic space.
problem Classifying ruled real hypersurfaces with constant norm.
method Analyzing nonflat complex space forms, proving existence and uniqueness.
result Existence of a unique inhomogeneous example in complex hyperbolic space.
Study proves existence and uniqueness for differential equations with non-Lipschitz coefficients.
problem Existence and uniqueness for differential equations with non-Lipschitz coefficients.
method Relying on robust Itô integration, prove existence and uniqueness results.
result Existence and uniqueness for one-dimensional differential equations with non-Lipschitz coefficients.
Proves existence and uniqueness of solutions for A_n tt*-Toda equations.
problem Existence and uniqueness of solutions for A_n tt*-Toda equations.
method Proof of existence and uniqueness for any n, new treatment of asymptotic data.
result Existence and uniqueness of global solutions for any n.
Proves existence and uniqueness of solutions to Lp Minkowski problem for electrostatic p-capacity.
problem Existence and uniqueness of solutions to Lp Minkowski problem for electrostatic p-capacity.
method Proved existence and uniqueness of solutions for specific ranges of p and p-capacity.
result Proves existence and uniqueness of solutions for Lp Minkowski problem for electrostatic p-capacity.
Study finds unique and non-existent constant mean curvature hypersurfaces in specific spacetimes.
problem Finding unique and non-existent constant mean curvature spacelike hypersurfaces.
method Geometric and physical assumptions applied to Generalized Robertson-Walker spacetimes.
result New uniqueness and non-existence results for complete spacelike hypersurfaces.
Pathwise uniqueness shown for specific stochastic equations.
problem Stochastic Volterra equations with singular kernels and Hölder coefficients.
method Established pathwise uniqueness through Hölder continuity of coefficients.
result Pathwise uniqueness and existence of unique strong solutions.
This paper surveys some recent results on existence, uniqueness and removable singularities for fully nonlinear differential equations on manifolds. The discussion also treats restriction theorems and the strong Bellman principle.
Proves existence of static vacuum metrics with specific boundary data.
problem Existence of static vacuum metrics with prescribed boundary data.
method Proves existence and local uniqueness of static vacuum metrics close to the Euclidean metric.
result Existence of static vacuum metrics with prescribed Bartnik boundary data.
We consider a class of finite Markov moment problems with arbitrary number of positive and negative branches. We show criteria for the existence and uniqueness of solutions, and we characterize in detail the non-unique solution families. Moreover, we present a constructive algorithm to solve the moment problems numeric…
Uniqueness of asymptotic limits for Ricci-flat manifolds with linear volume growth is proven.
problem Proving uniqueness of asymptotic limits for noncollapsed Ricci flat manifolds with linear volume growth.
method Relating uniqueness to the existence of a harmonic function asymptotic to a Busemann function, proving uniqueness via a monotone quantity.
result Proves uniqueness of the asymptotic limit and establishes a polynomial convergence rate.
Proves existence and uniqueness of loop equation solutions for semisimple Frobenius manifolds.
problem Existence and uniqueness of solutions to loop equations in generalized Frobenius manifolds.
method Proves existence and uniqueness of solutions to loop equations for semisimple generalized Frobenius manifolds.
result Existence and uniqueness of solutions to loop equations for semisimple generalized Frobenius manifolds.
Proves existence and uniqueness of weighted metrics for smooth spaces.
problem Existence and uniqueness of weighted metrics for smooth metric measure spaces.
method Proves existence and uniqueness using weighted ambient metrics and Poincaré metrics.
result Existence and uniqueness of weighted metrics for smooth metric measure spaces.
Study on heat equation and eigenfunctions on RCD spaces, proving unique continuation.
problem Unique continuation for caloric functions and eigenfunctions on RCD spaces.
method Establish weak unique continuation theorem for caloric functions and eigenfunctions on compact RCD(K,2) spaces.
result Existence of non-trivial eigenfunctions and caloric solutions vanishing up to infinite order at one point.
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.
In [3], the authors showed the existence and the uniqueness of a sl(m+1,\R)-equivariant quantization in the non-critical situations. The curved generalization of the sl(m+1,\R)-equivariant quantization is the natural and projectively equivariant quantization. In [1] and [7], the existence of such a quantization was pro…