Marston Morse | Academic Influence

Marston Morse's AcademicInfluence.com Rankings

Mathematics

#150

Historical Rank

Topology

#10

Historical Rank

Differential Geometry

#15

Historical Rank

Measure Theory

#287

Historical Rank

mathematics Degrees

Why Is Marston Morse Influential?

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According to Wikipedia, Harold Calvin Marston Morse was an American mathematician best known for his work on the calculus of variations in the large, a subject where he introduced the technique of differential topology now known as Morse theory. The Morse–Palais lemma, one of the key results in Morse theory, is named after him, as is the Thue–Morse sequence, an infinite binary sequence with many applications. In 1933 he was awarded the Bôcher Memorial Prize for his work in mathematical analysis.

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Marston Morse's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Papers

Symbolic Dynamics II. Sturmian Trajectories (1940) (835)
The Calculus of Variations in the Large (1934) (550)
Recurrent geodesics on a surface of negative curvature (371)
A fundamental class of geodesics on any closed surface of genus greater than one (238)
Relations between the critical points of a real function of $n$ independent variables (1925) (204)
Unending chess, symbolic dynamics and a problem in semigroups (1944) (190)
Science in the Modern World (1955) (117)
A reduction of the Schoenflies extension problem (1960) (106)
A One-to-One Representation of Geodesics on a Surface of Negative Curvature (103)
Topological methods in the theory of functions of a complex variable (1945) (76)
Singular quadratic functionals (1936) (70)
Singular Points of Vector Fields under General Boundary Conditions. (1928) (64)
A generalization of the sturm separation and comparison theorems inn-space (1930) (63)
On the Existence of Minimal Surfaces of General Critical Types. (1939) (59)
The Existence of Polar Non-Degenerate Functions on Differentiable Manifolds (1960) (54)
COMPLEX ANALYTIC MAPPINGS OF RIEMANN SURFACES I. (1960) (50)
THE CRITICAL POINTS OF A FUNCTION OF n VARIABLES. (1930) (47)
Manifolds without conjugate points (1942) (45)
Critical point theory in global analysis and differential topology : an introduction (1969) (44)
Variational analysis; critical extremals and Sturmian extensions (1973) (42)
C-Bimeasures Λ and Their Integral Extensions (1956) (40)
Functionals F Bilinear Over the Product A × B of Two Pseudo-Normed Vector Spaces: II. Admissible Spaces A (1950) (36)
Singular Points of Vector Fields Under General Boundary Conditions (1929) (35)
Bimeasures and their integral extensions (1955) (33)
Functional Topology and Abstract Variational Theory. (1937) (32)
Topologically non-degenerate functions on a compactn-manifoldM (1959) (31)
The Critical Point Theory Under General Boundary Conditions (1934) (30)
Functional Topology and Abstract Variational Theory. (1936) (29)
Unstable minimal surfaces of higher topological structure (1941) (24)
Introduction to analysis in the large (1957) (23)
Critical point theory under general boundary conditions (1936) (20)
A special parameterization of curves (1936) (20)
The calculus of variation in the large (1934) (20)
George David Birkhoff and his mathematical work (1946) (19)
Minimal Surfaces Not of Minimum Type by a New Mode of Approximation (1941) (18)
Schoenflies Extensions Without Interior Differential Singularities (1962) (18)
The Continuity of the Area of Harmonic Surfaces as a Function of the Boundary Representations (1941) (18)
Contour Equivalent Pseudoharmonic Functions and Pseudoconjugates (1952) (17)
HOMOTOPY AND HOMOLOGY RELATED TO THE SCHOENFLIES PROBLEM (1953) (17)
Sufficient Conditions in the Problem of Lagrange with Variable End Conditions (1931) (16)
The Foundations of a Theory of the Calculus of Variations in the Large in m-Space (Second Paper) (1930) (16)
Functionals of Bounded Frechet Variation (1949) (16)
Rank and Span in Functional Topology (1940) (15)
The foundations of a theory in the calculus of variations in the large (1928) (14)
An explicit solution of the Schoenflies extension problem. (1960) (13)
The existence of pseudoconjugates on Riemann surface (1952) (13)
The Problems of Lagrange and Mayer with Variable End Points (1931) (13)
The topology of pseudo-harmonic functions (1946) (13)
What is Analysis in the Large (1942) (12)
Mathematics in the Defense Program (1941) (12)
Topological Methods in the Theory of Functions of a Single Complex Variable I. Deformation Types of Locally Simple Plane Curves (1945) (12)
Bowls of a Non-Degenerate Function on a Compact Differentiable Manifold (1965) (12)
The dependence of the Schoenflies extension on an accessory parameter (1960) (12)
C-Bimeasures Λ and their superior integrals Λ (1955) (12)
A Characterization of Fields in the Calculus of Variations. (1932) (11)
The Analysis and Analysis Situs of Regular n-Spreads in (n + r)-Space. (1927) (11)
Trends in analysis (1951) (10)
Deformation classes of meromorphic functions and their extensions to interior transformations (1947) (10)
The elimination of critical points of a non-degenerate function on a differentiable manifold (1964) (10)
Integral Representations of Bilinear Functionals. (1949) (10)
Sufficient Conditions in the Problem of Lagrange with Fixed End Points (1931) (9)
Mathematics and the Arts (1959) (9)
THE BOWL THEOREM AND A MODEL NONDEGENERATE FUNCTION. (1964) (8)
The critical points of functions and the calculus of variations in the large (8)
Curve familiesF* locally the level curves of a pseudoharmonic function (1954) (8)
Diffeomorphisms of manifolds (1962) (8)
The foundations of a theory of the calculus of variations in the large in -space. II (1930) (8)
Contributions to Fourier Analysis. (1950) (7)
Semi-normed vector spaces with duals of integral type (1954) (7)
The foundations of the calculus of variations in the large in -space. I (1929) (7)
Sufficient conditions in the problem of Lagrange without assumptions of normalcy (1935) (7)
Equilibrium points of harmonic potentials (1970) (7)
Global Variational Analysis: Weierstrass Integrals on a Riemannian Manifold. (1976) (7)
The Foundations of the Calculus of Variations in the Large in m-Space (First Paper) (1929) (7)
Functionals F Bilinear over the Product A × B of Two P-Normed Vector Spaces (1949) (7)
A characterization of the bilinear sums associated with the classical second variation (1949) (6)
The index theorem in the calculus of variations (1938) (6)
THE DEPENDENCE OF THE SCHOENFLIES EXTENSION ON AN ACCESSORY PARAMETER (THE TOPOLOGICAL CASE). (1963) (6)
CLOSED EXTREMALS. (1929) (6)
Generalized Concavity Theorems. (1935) (6)
TOPOLOGICAL METHODS ON RIEMANN SURFACES PSEUDOHARMONIC FUNCTIONS (1953) (6)
DIFFERENTIABLE MAPPINGS IN THE SCHOENFLIES PROBLEM. (1958) (6)
The Order of Vanishing of the Determinant of a Conjugate Base. (1931) (6)
The Fréchet Variation and the Convergence of Multiple Fourier Series. (1949) (5)
Subordinate quadratic forms and their complementary forms. (1971) (5)
FIELDS OF GEODESICS ISSUING FROM A POINT. (1960) (5)
THE REPRESENTATION OF A C-BIMEASURE ON A GENERAL RECTANGLE. (1956) (5)
On Certain Invariants of Closed Extremals. (1934) (5)
Topologically nondegenerate functions (1975) (5)
Singular homology over $Z$ on topological manifolds (1969) (5)
A SINGULARITY IN THE SCHOENFLIES EXTENSION. (1960) (4)
Products of a C-Measure and a Locally Integrable Mapping (1957) (4)
The existence of vector function spaces with duals of integral type (1958) (4)
Diffeomorphism inducing automorphisms of π1(Tp) (1966) (4)
F-deformations and f-tractions. (1973) (4)
Conjugate Nets, Conformal Structure, and Interior Transformations on Open Riemann Surfaces. (1953) (4)
Report of the War Preparedness Committee (1940) (4)
The first variation in minimal surface theory (1940) (3)
Schoenflies extensions of analytic families of diffeomorphisms (1961) (3)
Topological Methods in the Theory of Functions of a Single Complex Variable: I. Deformation Types of Locally Simple Plane Curves. (1945) (3)
Does Instability Imply Transitivity? (1934) (3)
Homology Relations on Regular Orientable Manifolds. (1952) (3)
Analytic diffeomorphisms approximatingCm-diffeomorphisms (1962) (3)
A positive, lower semi-continuous, non-degenerate function on a metric space (1948) (3)
The schoenflies extension in the analytic case (1961) (3)
Topological Methods in the Theory of Functions of a Single Complex Variable: III. Casual Isomorphisms in the Theory of Pseudo-Harmonic Functions (1946) (3)
Unstable Minimal Surfaces of Higher Topological Types. (1940) (3)
The generalized Fréchet variation and Riesz-Young-Hausdorff type Theorems (1953) (2)
CONDITIONED DIFFERENTIABLE ISOTOPIES (1964) (2)
Elementary Quotients of Abelian Groups, and Singular Homology on Manifolds (1970) (2)
The international Congress in Oslo (1936) (2)
The Problems of Lagrange and Mayer Under General End Conditions. (1930) (2)
THE THEOREM OF RIEMANN-ROCH FOR ADJOINT SYSTEMS ON KÄHLERIAN VARIETIES (1953) (2)
Abstract Critical Sets. (1935) (2)
General end conditions (1934) (2)
Singular homology on an untriangulated manifold (1972) (2)
Nondegenerate real-valued differentiable functions. (1967) (2)
Tractions in critical point theory (1975) (2)
III. THE FRÉCHET VARIATION AND PRINGSHEIM CONVERGENCE OF DOUBLE FOURIER SERIES (1950) (2)
L-S-homotopy classes on the topological image of a projective plane (1949) (2)
BOUNDARY VALUES OF PARTIAL DERIVATIVES OF POISSON INTEGRAL (1961) (2)
Non-degenerate functions on abstract differentiable manifoldsMn (1967) (2)
Contributions to the Theory of Riemann Surfaces. (AM-30) (1953) (2)
Mathematics and the Maximum Scientific Effort in Total War (1943) (1)
Report of the War Preparedness Committee of the American Mathematical Society and Mathematical Association of America at the Chicago meeting (1941) (1)
The Variational Theory in the Large Including the Non-Regular Case--Second Paper (1943) (1)
Nondegenerate point pairs in global variational analysis (1976) (1)
Connectivities R(i) of Fréchet Spaces in Variational Topology. (1975) (1)
Conical singular points of diffeomorphisms (1961) (1)
A setting for a theorem of bott. (1970) (1)
Axial Presentations of Regular Arcs on M(n). (1972) (1)
Orientation of differentiable manifolds (1971) (1)
Three Theorems on the Envelop of Extremals. (1935) (1)
Global analysis - analysis on manifolds : dedicated to Marston Morse (1892-1976) (1983) (1)
Tubular presentations π of subsets of manifolds (1977) (1)
Harmonic extensions (1963) (1)
Conjugate points on a limiting extremal. (1976) (1)
Quadratic Forms Θ and Θ-Fibre-Bundles (1965) (1)
The local characterization of vector function spaces with duals of integral type (1958) (1)
Proof of a general theorem on the linear dependence of $p$ analytic functions of a single variable (1916) (1)
The Fréchet Variation, Sector Limits, and Left Decompositions (1950) (1)
The existence of non-degenerate functions on a compact differentiablem-manifoldM (1960) (1)
A new implication of the Young-Pollard convergence criteria for a Fourier series (1951) (1)
BOWLS, f-FIBER BUNDLES, AND THE ALTERATION OF CRITICAL VALUES. (1968) (1)
Focal sets of regular manifolds $M_{n-1}$ in $E_n$ (1967) (1)
Three theorems on the envelope of extremals (1936) (1)
Model families of quadratic forms. (1971) (1)
Mathematics, the Arts and Freedom (1959) (1)
THE REDUCTION OF A FUNCTION NEAR A NONDEGENERATE CRITICAL POINT. (1965) (1)
The fixed end point problem in non-parametric form (1934) (1)
International Congress of Mathematicians : Cambridge, Massachusetts, U.S.A. 1950 Conference in analysis (1950) (0)
Postcard from M. L. Morse to Joshua and Esther Lederberg (1957) (0)
Chapter III. Interior Transformations (1948) (0)
Errata: Differentiable Mappings in the Schoenflies Problem (1958) (0)
Chapter I. Pseudo-Harmonic Functions (1948) (0)
Occupational classification of mathematicians (1942) (0)
Mathematical Reviews (1939) (0)
Letter from M. L. Morse to Joshua Lederberg (1960) (0)
The index form (1934) (0)
Solution of the Poincaré continuation problem (1934) (0)
Science and the Library (1949) (0)
International Congress of Mathematicians (1932) (0)
Chapter IV. The General Order Theorem (1948) (0)
Selective Service for Mathematicians (1942) (0)
BINARY CONGRUENCES IN ALGEBRAIC NUMBER FIELDS BY ECKFORD COHEN (0)
Postcard from M. L. Morse to Joshua Lederberg (1956) (0)
The boundary problem in the large (1934) (0)
IV. NORMS OF DISTRIBUTION FUNCTIONS ASSOCIATED WITH BILINEAR FUNCTIONALS (1950) (0)
Tubular presentations pi of subsets of manifolds. (1977) (0)
André Weil Faculty file: correspondence, 1957-1959 (1959) (0)
Letter from M. L. Morse to Joshua and Esther Lederberg (1956) (0)
Chapter V. Deformations of Locally Simple Curves and of Interior Transformations (1948) (0)
Letter from M. L. Morse to Jean Weigle (1957) (0)
Letter from Marston Morse (1942) (0)
Chapter II. Differentiable Boundary Values (1948) (0)
The critical sets of functions (1934) (0)
BY EVERETT PITCHER THE SINGLE MOST SIGNIFICANT contribution of Marston Morse (0)

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