Reverse bubbling in geometric flows
نویسنده
چکیده
Reverse bubbling refers to singularities which develop in geometric flows as one takes a reverse limit t ↓ T rather than the traditional t ↑ T . Flows with this type of singularity may have different or better properties, and can provide alternative ways of flowing past singularities. We survey the original reverse bubbling theory for the harmonic map flow, including recent developments, and otherwise focus mainly on the various analogous phenomena for Ricci flow. 2000 Mathematics Subject Classification: 35K55 35K20 53C44 58J35 58J32 30C80
منابع مشابه
Bubbling and Regularity Issues in Geometric Non-linear Analysis
Numerous elliptic and parabolic variational problems arising in physics and geometry (Ginzburg-Landau equations, harmonic maps, Yang-Mills fields, Omega-instantons, Yamabe equations, geometric flows in general...) possess a critical dimension in which an invariance group (similitudes, conformal groups) acts. This common feature generates, in all these different situations, the same non-linear e...
متن کاملReverse Bubbling and Nonuniqueness in the Harmonic Map Flow
In this paper, we construct a new type of singularity which may occur in weak solutions of the harmonic map flow for two-dimensional domains. This " reverse bubbling " singu-larity may occur spontaneously, and enables us to construct solutions to the harmonic map heat equation which differ from the standard Struwe solution, despite agreeing for an arbitrarily long initial time interval.
متن کاملNewtonian and Non-Newtonian Blood Flow Simulation after Arterial Stenosis- Steady State and Pulsatile Approaches
Arterial stenosis, for example Atherosclerosis, is one of the most serious forms of arterial disease in the formation of which hemodynamic factors play a significant role. In the present study, a 3-D rigid carotid artery with axisymmetric stenosis with 75% reduction in cross-sectional area is considered. Laminar blood flow is assumed to have both Newtonian and non-Newtonian behavior (generalize...
متن کاملD-branes as a Bubbling Calabi-Yau
We prove that the open topological string partition function on aD-brane configuration in a Calabi-Yau manifoldX takes the form of a closed topological string partition function on a different Calabi-Yau manifold Xb. This identification shows that the physics of D-branes in an arbitrary background X of topological string theory can be described either by open+closed string theory in X or by clo...
متن کاملSharp estimates for fully bubbling solutions of a SU(3) Toda system
In this paper, we obtain sharp estimates of fully bubbling solutions of SU(3) Toda system in a compact Riemann surface. In geometry, the SU(n+1) Toda system is related to holomorphic curves, harmonic maps or harmonic sequences of the Riemann surface to CP. In order to compute the Leray-Schcuder degree for the Toda system, we have to obtain accurate approximations of the bubbling solutions. Our ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010