of differential geometry and geometric analysis, inverse mean curvature flow (IMCF) is a geometric flow of submanifolds of a Riemannian or pseudo-Riemannian...

In mathematics, the mean curvature H {\displaystyle H} of a surface S {\displaystyle S} is an extrinsic measure of curvature that comes from differential...

field of differential geometry in mathematics, mean curvature flow is an example of a geometric flow of hypersurfaces in a Riemannian manifold (for example...

He is known for foundational contributions to the theory of the mean curvature flow, including Huisken's monotonicity formula, which is named after him...

inverse mean curvature flow, which they developed. In 1999, Hubert Bray gave the first complete proof of the above inequality using a conformal flow of...

mean curvature flow Willmore flow, as in minimax eversions of spheres Inverse mean curvature flow Intrinsic geometric flows are flows on the Riemannian...

Craig Evans as supervisor. Ilmanen and Gerhard Huisken used inverse mean curvature flow to prove the Riemannian Penrose conjecture, which is the fifteenth...

_{t})\geq 0.} Said otherwise, Hawking mass is increasing for the inverse mean curvature flow. Hawking mass is not necessarily positive. However, it is asymptotic...

curvature tensor.[H95c] Hamilton's theorem, which requires strict convexity, is naturally applicable to certain singularities of mean curvature flow due...

generalized mean curvature flow equations. J. Differential Geom. 33 (1991), no. 3, 749–786. Huisken, Gerhard; Ilmanen, Tom. The inverse mean curvature flow and...

examples of vector flows include the geodesic flow, the Hamiltonian flow, the Ricci flow, the mean curvature flow, and Anosov flows. Flows may also be defined...

study the geodesic flow on Riemannian manifolds, starting with the results of Eberhard Hopf for Riemann surfaces of negative curvature. Markov chains form...

the Hubble flow of the expanding universe. The peculiar velocities of nonrelativistic particles decay as the universe expands, in inverse proportion with...

the airfoil is an impermeable surface, the flow w ( x ) {\displaystyle w(x)} must balance an inverse flow from V. By the small-angle approximation, V...

mass. Huisken had earlier initiated the study of volume-preserving mean curvature flow of hypersurfaces of Euclidean space. Huisken and Yau adapted his...

laminar flow in tubes where D {\displaystyle D} is the internal diameter, μ b {\displaystyle {\mu }_{b}} is the fluid viscosity at the bulk mean temperature...

the principal curvatures. Their average is called the mean curvature of the surface, and their product is called the Gaussian curvature. There are many...

resistance of an object is a measure of its opposition to the flow of electric current. The inverse quantity is electrical conductance, and is the ease with...

a right inverse of Exponential map. Mean curvature Metric ball Metric tensor Minimal surface is a submanifold with (vector of) mean curvature zero. Natural...

_{xx}+2|\varphi |^{2}\varphi =0} . The zero-curvature equation is so named as it corresponds to the curvature being equal to zero if it is defined F μ ν...

Moscicka-Grzesiak, H. Gruszka and M. Stroinski, ‘‘Influence of Electrode Curvature on Predischarge Phenomena and Electric Strength at 50 Hz of a Vacuum R...

liquid-vapor boundary is due to Laplace pressure, which is proportional to the mean curvature. Solving the above equation for both convex and concave surfaces yields:...

The driving force is the flow over the jug edge, so one might expect an edge-tone dipole sound field. In this case, The curvature and roundness of the edge...

(also called the principal normal), and r is its instantaneous radius of curvature based upon the osculating circle at time t. These components are called...

shadow at some distance from the source. The radius of curvature of the sound path is inversely proportional to the velocity gradient. A wind speed gradient...

the curvature of spacetime. These tidal accelerations are strictly local. It is the cumulative total effect of many local manifestations of curvature that...

of space and time, or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever...

asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received. When the price of...

function of the mean curvature of the interface at a given location at the surface, meaning the pressure is dependent on the two radii of curvature that give...

(and its curvature is high), these effects become very large in magnitude. The change in energy is much higher when the radius of curvature is less than...