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...Aleksandr Danilovich Aleksandrov]] and [[Aleksei Pogorelov]] on [[geodesic convexity|convex]] [[hypersurface]]s. In the 1980s fundamental contributions by [[Kar ...ry of partial differential equations to geometry. It incorporates problems involving curves and surfaces, or domains with curved boundaries, but also the study ...

=== Convexity === ...th> and <math>f_1</math> and a number <math>0 \le \lambda \le 1</math> the convexity relation ...

...of the given graph.<ref>{{harvtxt|Duchet|1987}}.</ref> For related results involving [[shortest path]]s instead of induced paths see {{harvtxt|Chepoi|1986}} and | title = Some properties of the d-convexity in triangulated graphs ...

{{About||more theorems that are called Riesz's theorem|Riesz theorem (disambiguation){{!}}Riesz th ...to as the '''Riesz–Thorin interpolation theorem''' or the '''Riesz–Thorin convexity theorem''', is a result about ''interpolation of operators''. It is named ...

The assumption of [[Locally convex topological vector space|local convexity]] for the ambient space is necessary, because {{harvs|first=James|last=Robe [[Category:Theorems involving convexity]] ...

[[File:Convex 01.ogg|thumb|right|Visualizing convexity and Jensen's inequality]] ...original points, which lies above the function itself by the definition of convexity. The conclusion follows.<ref>{{cite book |last=Bradley |first=CJ |date=2006 ...

==Fundamental theorems== *'''[[L'Hôpital's rule]]''' – uses derivatives to help evaluate limits involving indeterminate forms ...

...e satisfied. He also proved generalizations of the Birkhoff canonical form theorems for volume preserving mappings in n-dimensions and symplectic mappings, all ...re]]s and supplying rigorous (by present-day standards) proofs of his main theorems.<ref name=SingerSteinberg1965>{{Cite journal |last1=Singer |first1=I. M. |a ...

...''L^p'' in this case. Convexity fails but a kind of "''complex convexity''" remains, namely the fact that ''z'' → |''z''|^''q'' is [[Subha ...ate=February 2017}} The inner function can be further factored into a form involving a [[Blaschke product]]. ...

A [[differential equation]] is an equation involving an unknown function and its derivatives. ...ion theory]] is a branch of [[applied mathematics]] and [[social science]] involving the quantification of [[information]]. Historically, information theory was ...

...) {{ISBN|2-13-037495-6}}</ref> This gives it a place among the fundamental theorems of topology.<ref>More exactly, according to Encyclopédie Universalis: ''Il ===Convexity=== ...

| notable_ideas = Theorems on packings and coverings of geometrical objects, including the packing of | title = Some packing and covering theorems ...

...ity''' is a [[geometry|geometric]] [[inequality (mathematics)|inequality]] involving the square of the [[circumference]] of a [[closed curve]] in the plane and ...^n</math>. Under additional restrictions on the set (such as [[Convex set|convexity]], [[Closed regular set|regularity]], [[Smooth surface|smooth boundary]]), ...

...p : X \to \R</math> such that <math>|f| \leq p</math>; this last statement involving the linear functional <math>f</math> and seminorm <math>p</math> is encount ...ath>X / M</math> is isometrically isomorphic to <math>M^{\bot}.</math><ref>Theorems&nbsp;1.10.16, 1.10.17 pp.94–95 in {{harvtxt|Megginson|1998}}</ref> ...

The Bell numbers satisfy a [[recurrence relation]] involving [[binomial coefficient]]s:{{sfn|Wilf|1994|p=23}} | title = Bell numbers, log-concavity, and log-convexity ...

| ''A class of linear differential equations involving distributions'' ...st1=Embree|first1=Earl Owen|title=A class of linear differential equations involving distributions|date=1963|publisher=University of Illinois|location=Urbana-Ch ...

...athematical analysis]] illustrates that the value of certain infinite sums involving positive and negative summands depends on the order in which the summands a ...though this is nontrivial to establish.{{sfnm|1a1=Billingsley|1y=1995|1loc=Theorems 31.7 and 31.8 and p. 422}} In this definition, {{mvar|f}} is called the ''p ...

In the Christian faith, the [[liberation theology]] movement advocated involving the church in labor market capitalism. Many priests and nuns integrated the ...9580919|page =1012 |quote=Stiglitz criticizes the first and second welfare theorems for being based on the assumptions of complete markets (including a full se ...

| volume = 34}}</ref> and a common style of [[quilting]] involving the use of square quilt blocks.<ref>{{cite journal | title = Some surprising theorems about rectangles in triangles ...

...Mathematical logic|axioms]] that could be used to prove a broader class of theorems.<ref>{{cite encyclopedia |last=Von Plato |first=Jan |title=The Development By 1927, von Neumann was involving himself in discussions in Göttingen on whether [[elementary arithmetic]] fo ...