相关论文: Growth of balls of holomorphic sections and energy…

Let $\mathcal{O}(D)$ be an equivariant line bundle which is big and nef on a complex projective nonsingular toric variety $X$. Given a continuous toric metric $\|\cdot\|$ on $\mathcal{O}(D)$, we define the energy at equilibrium of…

Let $X$ be a compact Riemann surface and let $L$ be a positive line bundle on $X$. We obtain the growth speed of unit ball volume in $H^0(X,L^n)$ towards the energy at equilibrium. As an application, we also obtain the speed of Fekete…

Asymptotic behavior of energy of a harmonic map defined on an asymptotically hyperbolic manifold is considered. Using the growth of energy, we show that a harmonic map defined on some asymptotically hyperbolic manifolds has to be constant…

The Coulomb energy of a charge that is uniformly distributed on some set is maximized (among sets of given volume) by balls. It is shown here that near-maximizers are close to balls.

We study the effective behavior of heterogeneous energies arising in the modeling of material voids in geometrically linear elastic materials. Specifically, we consider functionals featuring bulk terms depending on the symmetrized gradient…

Energy bounds which are uniform in the background metric are obtained from upper bounds for entropy-like quantities. The argument is based on auxiliary Monge-Amp\`ere equations involving sublevel sets, and bypasses the…

Let $f$ be a $C^{1}$ diffeomorphism on a compact manifold $M$ admitting a partially hyperbolic splitting $TM=E^{s}\oplus_{\prec} E^{1}\oplus_{\prec} E^{2}\cdots \oplus_{\prec}E^{l}\oplus_{\prec} E^{u}$ where $E^{s}$ is uniformly…

Let $X$ be a normal projective variety over a complete discretely valued field and $L$ a line bundle on $X$. We denote by $X^\textrm{an}$ the analytification of $X$ in the sense of Berkovich and equip the analytification $L^\textrm{an}$ of…

We define a mass-type invariant for asymptotically hyperbolic manifolds with a noncompact boundary which are modelled at infinity on the hyperbolic half-space and prove a sharp positive mass inequality in the spin case under suitable…

Let $L$ be a big and semipositive line bundle on a complex projective manifold $X$, and let $\theta\in c_1(L)$ be a smooth semipositive representative. In the adjoint setting $H^0(X,L^k\otimes K_X)$, we prove that Donaldson's quantized…

A conformally invariant generalization of the Willmore energy for compact immersed submanifolds of even dimension in a Riemannian manifold is derived and studied. The energy arises as the coefficient of the log term in the renormalized area…

This paper extends the result of \cite{BM} on the homogenization of integral functionals with linear growth defined for Sobolev maps taking values in a given manifold. Through a $\Gamma$-convergence analysis, we identify the homogenized…

This is a survey of results concerning the asymptotic equilibrium distribution of zeros of random holomorphic polynomials and holomorphic sections of high powers of a positive line bundle, as related to the authors' recent work. Our primary…

Let X be a smooth complex projective variety of dimension d. It is classical that ample line bundles on X satisfy many beautiful geometric, cohomological, and numerical properties that render their behavior particularly tractable. By…

This paper is concerned with the existence, shape and dynamical stability of infinite-energy equilibria for a general class of spatially homogeneous kinetic equations in space dimensions $d \geq 3$. Our results cover in particular…

Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…

In higher dimensional gauge theory, we need energies with higher power terms of field strength in order to realize point-wise monopoles. We consider new models with higher power terms of field strength and extraordinary kinetic term of…

Using a result of Fujita on approximate Zariski decompositions and the singular version of Demailly's holomorphic Morse inequalities as obtained by Bonavero, we express the volume of a line bundle in terms of the absolutely continuous parts…

This paper investigates the asymptotic behavior of a class of nonlinear variational problems with Robin-type boundary conditions on a bounded Lipschitz domain. The energy functional contains a bulk term (the $p$-norm of the gradient), a…

We study thermodynamic formalism for topologically transitive partially hyperbolic systems in which the center-stable bundle satisfies a bounded expansion property, and show that every potential function satisfying the Bowen property has a…