arXiv research

Triangulates surfaces with bounded energy using diffeomorphisms.

Sharp bounds found for energy in projective space mappings.

Lower bounds on geodesic lengths for spheres with Willmore energy.

Quantizes Willmore energy in Riemannian manifolds with bounded energy and area.

Study energy-minimizing maps in projective spaces, proving sharp bounds.

Characterizes complex Hessian equations for bounded energy functions.

We give a unified statement and proof of a class of wellknown mean value inequalities for nonnegative functions with a nonlinear bound on the Laplacian. We generalize these to domains with boundary, requiring a (possibly nonlinear) bound on the normal derivative at the boundary. These inequalities give rise to an energ…

Researchers establish bounds and continuity of decomposed Möbius energies using cosine formula.

An energy estimate is proved for the Bel--Robinson energy along a constant mean curvature foliation in a spatially compact vacuum spacetime, assuming an $L^{\infty}$ bound on the second fundamental form, and a bound on a spacetime version of Bel--Robinson energy.

Signals are submanifolds; bounds on energy calculated.

Study lower bounds on modified K-energy on Fano manifolds with Kähler-Ricci solitons.

Proves energy quantization for surfaces with bounded index.

Study on harmonic maps from surfaces with energy bounds and neck domains.

Study bounds CMC surface index in 3-manifolds using energy.

A universal geometric inequality for bodies relating energy, size, angular momentum, and charge is naturally implied by Bekenstein's entropy bounds. We establish versions of this inequality for axisymmetric bodies satisfying appropriate energy conditions, thus lending credence to the most general form of Bekenstein's b…

For a bounded smooth domain in the plane and smooth boundary data we consider the minimisation of the Willmore functional for graphs subject to Dirichlet or Navier boundary conditions. For $H^2$-regular graphs we show that bounds for the Willmore energy imply area and diameter bounds. We then consider the $L^1$-lower s…

Bidirectional bounds stabilize training of energy-based models.

We study various aspects related to boundary regularity of complete properly embedded Willmore surfaces in H3, particularly those related to assumptions on boundedness or smallness of a certain weighted version of the Willmore energy. We prove, in particular, that small energy controls C1 boundary regularity. We examin…

Estimates for Schrödinger operators on manifolds with bounded Ricci curvature.

In this paper, we first prove a folklore conjecture on a greatest lower bound of the Calabi energy in all Kähler manifold. Similar result in algebriac setting was obtained by S. K. Donaldson. Secondly, we give an upper/lower bound estimate of the K energy in terms of the geodesic distance and the Calabi energy. This is…

In this paper, we establish compactness for various geometric curvature energies including integral Menger curvature, and tangent-point repulsive potentials, defined a priori on the class of compact, embedded $m$-dimensional Lipschitz submanifolds in ${\mathbb{R}}^n$. It turns out that due to a smoothing effect any seq…

In 1996, Shi generalized the epsilon-regularity theorem of Schoen and Uhlenbeck to energy-minimizing harmonic maps from a domain equipped with a bounded measurable Riemannian metric. In the present work we prove a compactness result for such energy-minimizing maps. As an application, we combine our result with Shi's th…

The Willmore energy of a closed surface in R^n is the integral of its squared mean curvature, and is invariant uner Möbius transformations of R^n. We show that any torus in R^3 with energy at most $8 π-delta$ has a representative under the Möbius action, for which the induced metric and a conformal metric of constant (…

The paper proves a Hawking-type singularity theorem using worldvolume quantum strong energy inequalities.

Bayesian model for energy-efficient EV navigation.

Using Perelman's results on Kahler Ricci flow, we prove that the K energy is bounded from below if and only if the F functional is bounded from below in the canonical Kahler class.

The fundamental properties of $J$-holomorphic maps depend on two inequalities: The gradient inequality gives a pointwise bound on the differential of a $J$-holomorphic map in terms of its energy. The cylinder inequality stipulates and quantifies the exponential decay of energy along cylinders of small total energy. We …

Stable solutions to a specific equation are one-dimensional.

In this paper, we prove that the Kahler Ricci flow converges to a Kahler Einstein metric when E_1 energy is small. We also prove that E_1 is bounded from below if and only if the K energy is bounded from below in the canonical class.

Optimizes energy efficiency in wireless sensor networks with limited information.

New $\varepsilon$-harmonic maps of low degree are rigid under certain energy bounds.

Study on bending energy of surfaces with curvature concentration, deriving new lower bounds.

Study bounds the index of minimal submanifolds using energy measures and Yang-Mills-Higgs equations.

The study extends calibrated geometry to smooth maps and finds energy bounds.

Proves convergence of gradient Ricci shrinkers with uniform bounds.

Bayesian model for energy consumption helps electric vehicles navigate efficiently.

We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. As an extension of Welling and Teh (2001), we define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals and derive an …

Optimizes energy of mappings from complex projective spaces.

We prove existence and a.e. regularity of an area minimizing soap film with a bound on energy spanning a given Jordan curve in R^3. The energy of a film is defined to be the sum of its surface area and the length of its singular branched set. The class of surfaces over which area is minimized includes images of disks, …

Study quantizes energy distribution in inhomogeneous phase transitions.

Geodesics found in a metric space of m-subharmonic functions.

We consider a vector bundle $E$ over a compact Riemannian manifold $M$=$M^{n}$,$n\geq 4$,and $A$ is a Yang-Mills connection with $L^{\frac{n}{2}}$ curvature $F_{A}$ on $E$.Then we prove a mean value inequality for the density $|F_{A}|^{\frac{n}{2}}$.This inequality give rise to an energy concentrate principle for seque…

Study gradient flow of phase transitions with fixed contact angle.

The paper proves a finite diffeomorphism theorem for manifolds with lower Ricci curvature and bounded energy.

We investigate knot-theoretic properties of geometrically defined curvature energies such as integral Menger curvature. Elementary radii-functions, such as the circumradius of three points, generate a family of knot energies guaranteeing self-avoidance and a varying degree of higher regularity of finite energy curves. …

We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. We define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals, derive a lower and an upper bound on the fractional Beth…

Develops a PDE approach to constructing nontrivial anisotropic surfaces.

We show the existence of a thick thin decomposition of the domain of a pseudo holomorphic curve with boundary. The geometry of the thick part is bounded uniformly in the energy. Furthermore, in the thick part, there is a uniform bound on the differential which is exponential in the energy. The thin part consists of ann…