Geometric inequalities | Differential geometry | Theorems in Riemannian geometry
Myers's theorem, also known as the Bonnet–Myers theorem, is a celebrated, fundamental theorem in the mathematical field of Riemannian geometry. It was discovered by Sumner Byron Myers in 1941. It asserts the following: Let be a complete Riemannian manifold of dimension whose Ricci curvature satisfies for some positive real number Then any two points of M can be joined by a geodesic segment of length at most In the special case of surfaces, this result was proved by Ossian Bonnet in 1855. For a surface, the Gauss, sectional, and Ricci curvatures are all the same, but Bonnet's proof easily generalizes to higher dimensions if one assumes a positive lower bound on the sectional curvature. Myers' key contribution was therefore to show that a Ricci lower bound is all that is needed to reach the same conclusion. (Wikipedia).
What is the max and min of a horizontal line on a closed interval
👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
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👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
Determine the extrema of a function on a closed interval
👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
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👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
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👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
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👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
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👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
My video on Sesame Studios: https://www.youtube.com/watch?v=BTjAiyyG2sw The Curiosity Box by Vsauce: https://www.curiositybox.com/ LINKS TO SOURCES BELOW! My twitter: https://twitter.com/tweetsauce My instagram: https://www.instagram.com/electricpants DONG: https://www.youtube.com/dong M
From playlist Knowledge
DEFCON 19: Weaponizing Cyberpsychology and Subverting Cybervetting for Fun, Profit and Subterfuge
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T. Richard - Lower bounds on Ricci curvature, with a glimpse on limit spaces (Part 1)
The goal of these lectures is to introduce some fundamental tools in the study of manifolds with a lower bound on Ricci curvature. We will first state and prove the laplacian comparison theorem for manifolds with a lower bound on the Ricci curvature, and derive some important consequences
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
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The goal of these lectures is to introduce some fundamental tools in the study of manifolds with a lower bound on Ricci curvature. We will first state and prove the laplacian comparison theorem for manifolds with a lower bound on the Ricci curvature, and derive some important consequences
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
T. Richard - Lower bounds on Ricci curvature, with a glimpse on limit spaces (Part 3)
The goal of these lectures is to introduce some fundamental tools in the study of manifolds with a lower bound on Ricci curvature. We will first state and prove the laplacian comparison theorem for manifolds with a lower bound on the Ricci curvature, and derive some important consequences
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
T. Richard - Lower bounds on Ricci curvature, with a glimpse on limit spaces (Part 4)
The goal of these lectures is to introduce some fundamental tools in the study of manifolds with a lower bound on Ricci curvature. We will first state and prove the laplacian comparison theorem for manifolds with a lower bound on the Ricci curvature, and derive some important consequences
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
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From playlist Journées Sous-Riemanniennes 2018
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👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
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Discussion Meeting: Entanglement from Gravity(URL: http://www.icts.res.in/discussion_meeting/EG2014/) Dates: Wednesday 10 Dec, 2014 - Friday 12 Dec, 2014 Description: In the last few years, quantum entanglement considerations have led to profound insights in the connection with gravity.
From playlist Discussion Meeting: Entanglement from Gravity
PhDads: Doug Myers Discusses Rattlesnakes
Ed Myers is a Gerstner Postdoctoral Fellow studying the evolution of venom in rattlesnakes. For Father’s Day, we asked his dad Doug a few questions about his son’s research. Then we played the call back for Ed. Follow @AMNH on Twitter to watch all the PhDad conversations on Father's Day,
From playlist PhDads: Researchers' Dads Explain Science For Father's Day
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👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
Ian Agol, Lecture 3: Applications of Kleinian Groups to 3-Manifold Topology
24th Workshop in Geometric Topology, Calvin College, June 30, 2007
From playlist Ian Agol: 24th Workshop in Geometric Topology