Hodge theory in the Sobolev topology for the de Rham complex on a smoothly bounded domain in Euclidean space.
Holomorphic Vector Fields with Simple Isolated Zeros.
Holonomy, twisting cochains and characteristic classes
This paper contains a description of various geometric constructions associated with fibre bundles, given in terms of important algebraic object, the “twisting cochain". Our examples include the Chern-Weil classes, the holonomy representation and the so-called cyclic Chern character of Bismut and others (see [2, 11, 27]), also called the Bismut’s class. The later example is the principal one for us, since we are motivated by the attempt to find an algebraic approach to the Witten’s index formula....
Homogeneous bundles and the first eigenvalue of symmetric spaces
In this note we prove the stability of the Gieseker point of an irreducible homogeneous bundle over a rational homogeneous space. As an application we get a sharp upper estimate for the first eigenvalue of the Laplacian of an arbitrary Kähler metric on a compact Hermitian symmetric spaces of ABCD–type.
Homological index formulas for elliptic operators over C*-algebras.
Homologie associée à une fonctionnelle
Homologie de l'algèbre quantique des symboles pseudo-différentiels sur le cercle
Homotopy and Homology Vanishing Theorems and the Stability of Stochastic Flows.
Homotopy invariance of relative eta-invariants and -algebra -theory.
Homotopy invariance of twisted higher signatures on manifolds with boundary
Horizontal martingales in vector bundles
How to produce a Ricci flow via Cheeger–Gromoll exhaustion
We prove short time existence for the Ricci flow on open manifolds of non-negative complex sectional curvature without requiring upper curvature bounds. By considering the doubling of convex sets contained in a Cheeger–Gromoll convex exhaustion and solving the singular initial value problem for the Ricci flow on these closed manifolds, we obtain a sequence of closed solutions of the Ricci flow with non-negative complex sectional curvature which subconverge to a Ricci flow on the open manifold. Furthermore,...
How to unify the total/local-length-constraints of the gradient flow for the bending energy of plane curves
The gradient flow of bending energy for plane curve is studied. The flow is considered under two kinds of constraints; one is under the area and total-length constraints; the other is under the area and local-length constraints. The fundamental results (the local existence and uniqueness) were obtained independently by Kurihara and the second author for the former one; by Okabe for the later one. For the former one the global existence was shown for any smooth initial curves, but the asymptotic...
Huygens’ principle and equipartition of energy for the modified wave equation associated to a generalized radial Laplacian
In this paper we consider the modified wave equation associated with a class of radial Laplacians generalizing the radial part of the Laplace-Beltrami operator on hyperbolic spaces or Damek-Ricci spaces. We show that the Huygens’ principle and the equipartition of energy hold if the inverse of the Harish-Chandra -function is a polynomial and that these two properties hold asymptotically otherwise. Similar results were established previously by Branson, Olafsson and Schlichtkrull in the case of...
Huyghens' principle in Riemannian symmetric spaces.
Hybrid matrix models and their population dynamic consequences
In this paper, the main purpose is to reveal what kind of qualitative dynamical changes a continuous age-structured model may undergo as continuous reproduction is replaced with an annual birth pulse. Using the discrete dynamical system determined by the stroboscopic map we obtain an exact periodic solution of system with density-dependent fertility and obtain the threshold conditions for its stability. We also present formal proofs of the supercritical flip bifurcation at the bifurcation as well...
Hybrid matrix models and their population dynamic consequences
In this paper, the main purpose is to reveal what kind of qualitative dynamical changes a continuous age-structured model may undergo as continuous reproduction is replaced with an annual birth pulse. Using the discrete dynamical system determined by the stroboscopic map we obtain an exact periodic solution of system with density-dependent fertility and obtain the threshold conditions for its stability. We also present formal proofs of the supercritical flip bifurcation at the bifurcation as...
Hyperbolic inverse mean curvature flow
We prove the short-time existence of the hyperbolic inverse (mean) curvature flow (with or without the specified forcing term) under the assumption that the initial compact smooth hypersurface of () is mean convex and star-shaped. Several interesting examples and some hyperbolic evolution equations for geometric quantities of the evolving hypersurfaces are shown. Besides, under different assumptions for the initial velocity, we can get the expansion and the convergence results of a hyperbolic...
Hyperbolic methods for Einstein's equations.
Hyper-differential operators in complex space