{"product_id":"9781470466961-the-space-of-spaces-curvature-boun","title":"The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces","description":"\u003cmeta content=\"text\/html; charset=utf-8\" http-equiv=\"Content-Type\"\u003e\u003cp\u003e\u003cspan\u003eEquipped with the \u003ci\u003eL\u003c\/i\u003e\u003csup\u003e2,\u003ci\u003eq\u003c\/i\u003e\u003c\/sup\u003e-distortion distance ??\u003csub\u003e2,\u003ci\u003eq\u003c\/i\u003e\u003c\/sub\u003e, this publication proves the space ??\u003csub\u003e2,\u003ci\u003eq\u003c\/i\u003e\u003c\/sub\u003e of all metric measure spaces to have nonnegative curvature in the sense of Alexandrov, characterising geodesics and tangent spaces in detail.\u003cbr\u003eEquipped with the \u003ci\u003eL\u003c\/i\u003e\u003csup\u003e2,\u003ci\u003eq\u003c\/i\u003e\u003c\/sup\u003e-distortion distance 𝚫\u003csub\u003e2,\u003ci\u003eq\u003c\/i\u003e\u003c\/sub\u003e, the space 𝕏\u003csub\u003e2,\u003ci\u003eq\u003c\/i\u003e\u003c\/sub\u003e of all metric measure spaces (\u003ci\u003eX\u003c\/i\u003e, ｄ, 𝔪) is proven to have nonnegative curvature in the sense of Alexandrov. Geodesics and tangent spaces are characterized in detail. Moreover, classes of semiconvex functionals and their gradient flows on ̅𝕏\u003csub\u003e2,\u003ci\u003eq\u003c\/i\u003e\u003c\/sub\u003e are presented.\u003cbr\u003e\u003cbr\u003e\u003c\/span\u003e\u003c\/p\u003e","brand":"Rarewaves","offers":[{"title":"Default Title","offer_id":55110066930038,"sku":"9781470466961","price":68.38,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0092\/7504\/8033\/files\/orig_36045616_a811eff4-46fc-472a-b57a-df6487d07379.jpg?v=1757580579","url":"https:\/\/www.rarewaves.com\/products\/9781470466961-the-space-of-spaces-curvature-boun","provider":"Rarewaves.com","version":"1.0","type":"link"}