Blogs about: Mathdg
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The concept of mass in General Relativity and its applications
Hi! Today I’m posting an expanded version of an informal talk (directed to PhD students at IMPA) I gave in January 21, 2005 about the so-called ADM mass in General Relativity and its application… more →
Disquisitiones Mathematicae
The concept of mass in General Relativity and its applications
matheuscmss wrote 1 month ago: Hi! Today I’m posting an expanded version of an informal talk (directed to PhD students at IMP … more →
Differential Geometry
camnc wrote 6 months ago: At the time of this posting, there is still a question on the boards without a single solution. Tha … more →
What is a gauge?
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Terence Tao wrote 1 year ago: “Gauge theory” is a term which has connotations of being a fearsomely complicated part o … more →
Classification of Almost Quarter-Pinched Manifolds
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Terence Tao wrote 1 year ago: Peter Petersen and I have just uploaded to the arXiv our paper, “Classification of Almost Quar … more →
Bohm and Wilking's method of deformation of Ricci flow invariant curvature conditions
matheuscmss wrote 1 year ago: In a previous post about the proof of the differentiable sphere theorem (due to S. Brendle and R. Sc … more →
Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class
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Terence Tao wrote 1 year ago: I have just uploaded to the arXiv the second installment of my “heatwave” project, entit … more →
The differentiable sphere theorem of Brendle and Schoen
matheuscmss wrote 1 year ago: A fundamental problem in Differential Geometry is the following: Problem. Determine the topology of … more →
285G, Lecture 19: The structure of Ricci flow at the singular time, surgery, and the Poincaré conjecture
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Terence Tao wrote 1 year ago: In the previous lecture, we studied high curvature regions of Ricci flows on some time interval , an … more →
285G, Lecture 18: The structure of high-curvature regions of Ricci flow
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Terence Tao wrote 1 year ago: Having characterised the structure of -solutions, we now use them to describe the structure of high … more →
285G, Lecture 17: The structure of κ-solutions
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Terence Tao wrote 1 year ago: Having classified all asymptotic gradient shrinking solitons in three and fewer dimensions in the pr … more →
285G, Lecture 16: Classification of asymptotic gradient shrinking solitons
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Terence Tao wrote 1 year ago: In the previous lecture, we showed that every -solution generated at least one asymptotic gradient s … more →
285G, Lecture 15: Geometric limits of Ricci flows, and asymptotic gradient shrinking solitons
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Terence Tao wrote 1 year ago: We now begin using the theory established in the last two lectures to rigorously extract an asymptot … more →
285G, Lecture 14: Stationary points of Perelman entropy or reduced volume are gradient shrinking solitons
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Terence Tao wrote 1 year ago: We continue our study of -solutions. In the previous lecture we primarily exploited the non-negative … more →
285G, Lecture 12: High curvature regions of Ricci flow and κ-solutions
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Terence Tao wrote 1 year ago: In previous lectures, we have established (modulo some technical details) two significant components … more →
285G, Lecture 11: κ-noncollapsing via Perelman reduced volume
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Terence Tao wrote 1 year ago: Having established the monotonicity of the Perelman reduced volume in the previous lecture (after fi … more →
285G, Lecture 10: Variation of L-geodesics, and monotonicity of Perelman reduced volume
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Terence Tao wrote 1 year ago: Having completed a heuristic derivation of the monotonicity of Perelman reduced volume (Conjecture 1 … more →
285G, Lecture 9: Comparison geometry, the high-dimensional limit, and Perelman reduced volume
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Terence Tao wrote 1 year ago: We now turn to Perelman’s second scale-invariant monotone quantity for Ricci flow, now known a … more →
285G, Lecture 8: Ricci flow as a gradient flow, log-Sobolev inequalities, and Perelman entropy
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Terence Tao wrote 1 year ago: It is well known that the heat equation (1) on a compact Riemannian manifold (M,g) (with metric g st … more →
285G, Lecture 7: Rescaling of Ricci flows and κ-noncollapsing
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Terence Tao wrote 1 year ago: We now set aside our discussion of the finite time extinction results for Ricci flow with surgery (T … more →
