Titlebook: Brakke‘s Mean Curvature Flow; An Introduction Yoshihiro Tonegawa Book 2019 The Author(s), under exclusive license to Springer Nature Singap

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https://doi.org/10.1007/978-3-642-18720-9.) at .?∈?.(.). Here we consider how one may characterize the normal velocity using integration. The reason for such a pursuit is that, in the end, we want to replace .(.) by a general varifold. To do so, let . be a non-negative “test function”.

Monotonous

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冷漠

Definition of the Brakke Flow,.) at .?∈?.(.). Here we consider how one may characterize the normal velocity using integration. The reason for such a pursuit is that, in the end, we want to replace .(.) by a general varifold. To do so, let . be a non-negative “test function”.

彈藥

A General Existence Theorem for a Brakke Flow in Codimension One, some minor assumption, Brakke gave a proof of a time-global existence of rectifiable Brakke flow starting from the given data. When the initial data is an integral .-varifold, the obtained flow is also integral in the sense defined in Chap. ..

pulmonary

Allard Regularity Theory,ose that we have a varifold .?∈..(.) which happens to be a time-independent Brakke flow as we defined in Sect. .. This should mean that the normal velocity . is 0 and that .?=?. implies .?=?0, which means that .?is stationary. Let us adhere to the definition of the Brakke flow as in Definition . and check if this is indeed the case.

Herbivorous

Yoshihiro TonegawaIs the first exposition of Brakke’s mean curvature flow, a subject that interests many researchers.Uses accessible language, not highly technical terminology, for all readers interested in geometric m

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