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

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

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

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

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

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...

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

_{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...

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...

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...

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

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...

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

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...

1989. Guilfoyle, B.; Klingenberg, W. (2019). "Higher codimensional mean curvature flow of compact spacelike submanifolds". Trans. Amer. Math. Soc. 372 (9):...

(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...

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

_{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...

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:...

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...

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

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

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

associated Riemann-Hilbert boundary value problem, and then applies mean curvature flow and the Sard–Smale Theorem on regular values of Fredholm operators...

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

tension γ {\displaystyle \gamma } and H f {\displaystyle H_{f}} the mean curvature. This suppresses small-wavelength (high-wavenumber) disturbances, and...

space-time curvature is evolving lock-step with the others. This presents a mystery: how did these new regions know what temperature and curvature they were...

four-dimensional spacetime, and the flow of time changes depending on the curvature of spacetime and the spacetime trajectory of the observer. How can these...