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arXiv research

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2 results for “H-bubble”

Finite-time singularity formation for the heat flow of the

H

-systemmath.AP

Researchers found a new type of singularity in surface evolution equations.

problem Finite-time singularity formation in surface evolution equations.

method Constructed first example of finite time blow-up solutions for the heat flow of the H-system.

result Singularity forms as a scaled least energy H-bubble with decoupled linearized operators.

finite-time singularity H-system surface evolution blow-up solutions H-bubble

2023-11-24abs ↗pdf ↗

A note on the existence of H-bubbles via perturbation methodsmath.AP

We study the problem of existence of surfaces in ${\bf R}^3$ parametrized on the sphere ${\mathbb S}^2$ with prescribed mean curvature $H$ in the perturbative case, i.e. for $H=H_0+εH_1$ , where $H_0$ is a nonzero constant, $H_1$ is a $C^2$ function and $ε$ is a small perturbation parameter.

2003-01-23abs ↗pdf ↗