Integrals of Subharmonic Functions on Manifolds of Nonnegative Curvature.
Integration in a dynamical stochastic geometric framework
Motivated by the well-posedness of birth-and-growth processes, a stochastic geometric differential equation and, hence, a stochastic geometric dynamical system are proposed. In fact, a birth-and-growth process can be rigorously modeled as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth dynamics, respectively. The simplicity of the proposed geometric approach allows to avoid problems of boundary...
Integration in a dynamical stochastic geometric framework
Motivated by the well-posedness of birth-and-growth processes, a stochastic geometric differential equation and, hence, a stochastic geometric dynamical system are proposed. In fact, a birth-and-growth process can be rigorously modeled as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth dynamics, respectively. The simplicity of the proposed geometric approach allows to avoid problems of boundary...
Integration Near the Royden Boundary of a Riemannian Manifold.
Integration of a density and the fiber integral for regular Lie algebroids in a nonorientable case
Integration of Monge-Ampère equations and surfaces with negative gaussian curvature
Integrity basis for a second-order and a fourth-order tensor.
Interaction of Tubes and Spheres.
Interface dynamics for an anisotropic Allen-Cahn equation
Interior curvature estimates for hypersurfaces of prescribed mean curvature
Interior estimates for hypersurfaces moving by mean curvature.
Interior estimates for solutions of Abreu's equation.
This paper develops various estimates for solutions of a nonlinear, fouth order PDE which corresponds to prescribing the scalar curvature of a toric Kähler metric. The results combine techniques from Riemannian geometry and from the theory of Monge-Ampère equations.
Intermediate flexibility of surfaces
Intermediate inversion formulas in integral geometry.
Interpolation of Banach spaces, differential geometry and differential equations.
In recent years the study of interpolation of Banach spaces has seen some unexpected interactions with other fields. (...) In this paper I shall discuss some more interactions of interpolation theory with the rest of mathematics, beginning with some joint work with Coifman [CS]. Our basic idea was to look for the methods of interpolation that had interesting PDE's arising as examples.
Intersection pairings in moduli spaces of holomorphic bundles on a Riemann surface.
Intersections in hyperbolic manifolds.
Intertwinors on functions over the product of spheres.
Intrinsic geometric on the class of probability densities and exponential families.
We present a way of thinking of exponential farnilies as geodesic surfaces in the class of positive functions considered as a (multiplicative) sub-group G+ of the group G of all invertible elements in the algebra A of all complex bounded functions defined on a measurable space. For that we have to study a natural geometry on that algebra. The class D of densities with respect to a given rneasure will happen to be representatives of equivalence classes defining a projective space in A. The natural...
Intrinsic measures complex manifolds