11 citations · 13 across the 7 of their papers we have counts for
7 papers
Concentration of the first eigenfunction for a second order elliptic operator
D. Holcman, I. Kupka
We study the semi-classical limits of the first eigenfunction of a positive second order operator on a compact Riemannian manifold when the diffusion constant goes to zero. We…
The survival probability of diffusion with killing
D. Holcman, A. Marchewka, Z. Schuss
We present a general framework to study the effect of killing sources on moving particles, trafficking inside biological cells. We are merely concerned with the case of spine-dendr…
The Boundary between Compact and Noncompact Complete Riemann Manifolds
D. Holcman, C. Pugh
In 1941 Sumner Myers proved that if the Ricci curvature of a complete Riemann manifold has a positive infimum then the manifold is compact and its diameter is bounded in terms of t…
Singular perturbation for the first eigenfunction and blow up analysis
David Holcman, Ivan Kupka
On a compact Riemannian manifold (V_{m},g), we consider the second order positive operator L_ε = εΔ_{g} +(b,\nabla) +c, where -Δ_{g} is the Laplace-Beltrami operator and b is a Mor…
Narrow Escape, Part III: Riemann surfaces and non-smooth domains
A. Singer, Z. Schuss, D. Holcman
We consider Brownian motion in a bounded domain on a two-dimensional Riemannian manifold . We assume that the boundary $\pΩ$ is smooth and reflects the trajectories, exc…
Narrow Escape, Part II: The circular disk
A. Singer, Z. Schuss, D. Holcman
We consider Brownian motion in a circular disk , whose boundary $\pΩ$ is reflecting, except for a small arc, $\pΩ_a$, which is absorbing. As decr…