arXiv research

No finite-time singularities in Yang-Mills flow in 4D.

New energy identity found for biharmonic maps into spheres.

Study geodesic X-ray transforms on curved manifolds using Carleman estimates.

A new energy-efficient pruning method for federated learning.

The paper extends energy identities and neck existence for ε-harmonic maps.

The paper proves an energy identity for Dirac-harmonic maps from surfaces with boundary.

Paper proves energy identity and no-neck property for special harmonic maps.

Study proves neck properties for smooth maps with bounded energy.

We describe a new interpretation of the fractional GJMS operators as generalized Dirichlet-to-Neumann operators associated to weighted GJMS operators on naturally associated smooth metric measure spaces. This gives a geometric interpretation of the Caffarelli--Silvestre extension for $(-Δ)^γ$ when $γ\in(0,1)$, and both…

We consider in dimension four weakly convergent sequences of approximate biharmonic maps to a Riemannian manifold with bi-tension fields bounded in $L^p$ for $p>\frac43$. We prove an energy identity that accounts for the loss of hessian energies by the sum of hessian energies over finitely many nontrivial biharmonic ma…

The identity map of certain Einstein manifolds is stable in both energy and bienergy.

Characterizes low energy behavior of fibered Dirac operators.

Study of energy quantization in a nonlinear sigma model with critical gravitinos.

We prove an energy identity for anti-self-dual connections on the product C\timesΣof the complex plane and a Riemann surface. The energy is a multiple of a basic constant that is determined from the values of a corresponding Chern-Simons functional on flat connections and its ambiguity under gauge transformations. For …

We construct a closed Riemannian manifold $(N,h)$ and a sequence of $α$-harmonic maps from $S^2$ into $N$ with uniformly bounded energy such that the energy identity for this sequence is not true.

We consdier in dimension four weakly convergent sequences of approximate biharmonic maos into sphere with bi-tension fields bounded in $L^p$ for some $p>1$. We prove an energy identity that accounts for the loss of Hessian energies by the sum of Hessian energies over finitely many nontrivial biharmonic maps on $\mathbb…

We will give a weak energy identity for Sacks-Uhlenbeck approximation of harmonic maps and calculate the length of the necks.

Extends denoising and score estimation to energy models via Tweedie's formula.

The paper examines Yang-Mills-Higgs pairs on vector bundles and proves stability and energy identity.

The paper proves an energy identity for harmonic maps near singularities.

Study existence of harmonic and Dirac-harmonic maps from degenerating surfaces.

Derives stress-energy identities in Liouville theory on compact surfaces.

The paper proves a gap theorem for special harmonic maps between spheres.

We prove that the Yang-Mills $α$-functional satisfies the Palais-Smale condition. This guarantees the existence of critical points, which are called Yang-Mills $α$-connections. It was shown by Hong, Tian and Yin in [10] (to appear in Comm. Math. Helv.) that as $α\to 1$, a sequence of Yang-Mills $α$-connections converge…

We prove the energy identity for min-max sequences of the Sacks-Uhlenbeck and the biharmonic approximation of harmonic maps from surfaces into general target manifolds. The proof relies on Hopf-differential type estimates for the two approximations and on estimates for the concentration radius of bubbles.

Let $u_n$ be a sequence of mappings from a closed Riemannian surface $M$ to a general Riemannian manifold $N$. If $u_n$ satisfies \beno \sup_{n}\big(\|\nabla u_n\|_{L^2(M)}+\|τ(u_n)\|_{L^{p}(M)}\big)\leq Λ\quad \text{for some}\,\,p>1, \eeno where $τ(u_n)$ is the tension field of $u_n$, then there hold the so called ene…

Bayesian weight priors improve neural network learning of identity relations.

The paper extends a theorem and studies the convergence of branched conformal immersions with bounded areas and Willmore energies.

Proves convergence of gradient Ricci shrinkers with uniform bounds.

Paper extends positive energy theorem to anti-de Sitter spacetimes.

Optimal Euclidean structure minimizes energy in weighted toroidal graphs.

Gradient descent recovers planted weights in shallow neural networks with quadratic activations.

We derive global estimates in critical scale invariant norms for solutions of elliptic systems with antisymmetric potentials and almost holomorphic Hopf differential in two dimensions. Moreover we obtain new energy identities in such norms for sequences of solutions of these systems. The results apply to harmonic maps …

Paper proposes MCMA architecture for neural approximate computing with higher invocation rate and energy savings.

Weak Bianchi identity found for spacetimes with timelike singularities.

New method trains quantized neural networks to global optimality.

Study investigates singularity formation in $\alpha$-Yang-Mills-Higgs fields on spheres.

The study examines the behavior of maps near the boundary of surfaces.

Proves weight polytope matches with energy vectors in toric varieties.

Let $M$ be a closed Riemannian surface and $u_n$ a sequence of maps from $M$ to Riemannian manifold $N$ satisfying $\sup_n(\|\nabla u_n\|_{L^2(M)}+\|τ(u_n)\|_{L^p(M)})\leq Λ$ for some $p>1$, where $τ(u_n)$ is the tension field of the mapping $u_n$. For the general target manifold $N$, if $p\geq \frac 65$, we prove th…

Under a spectral assumption on the Laplacian of a Poincaré--Einstein manifold, we establish an energy inequality relating the energy of a fractional GJMS operator of order $2γ\in(0,2)$ or $2γ\in(2,4)$ and the energy of the weighted conformal Laplacian or weighted Paneitz operator, respectively. This spectral assumption…

We study a new set of coupled field equations motivated by the non-linear supersymmetric sigma model of quantum field theory. These equations couple a map into a Riemannian manifold controlled by a harmonic map like action with a spinor field along that map. We study the solutions which we call Dirac-harmonic maps from…

Study quantizes energy for a specific fourth-order system in 4D.

This paper generalizes neural transport learning for free energy estimation in arbitrary state spaces.

Study extends eigenvalue formulas to weighted manifolds and proves global rigidity theorems.

Generative diffusion models mimic biological memory networks, encoding associative dynamics in deep neural weights.

We study harmonic maps from degenerating Riemann surfaces with uniformly bounded energy and show the so-called generalized energy identity. We find conditions that are both necessary and sufficient for the compactness in $W^{1,2}$ and $C^{0}$ modulo bubbles of sequences of such maps.

New class of heavy-tailed distributions shows weighted averages dominate individual variables.