Class information for:
Level 1: MONGE AMPERE EQUATION//HESSIAN EQUATION//BERNSTEIN PROPERTY

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
17113 617 17.3 43%


Bar chart of Publication_year

Last years might be incomplete

Hierarchy of classes
The table includes all classes above and classes immediately below the current class.


Cluster id Level Cluster label #P
15 4 MATHEMATICS//MATHEMATICS, APPLIED//MATH 719832
94 3       MATHEMATICS//MATHEMATICS, APPLIED//MATH 76582
291 2             MATHEMATICS//ANNALS OF GLOBAL ANALYSIS AND GEOMETRY//DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS 18882
17113 1                   MONGE AMPERE EQUATION//HESSIAN EQUATION//BERNSTEIN PROPERTY 617

Terms with highest relevance score


rank Term termType Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 MONGE AMPERE EQUATION authKW 507711 8% 21% 49
2 HESSIAN EQUATION authKW 375064 2% 63% 12
3 BERNSTEIN PROPERTY authKW 346422 1% 100% 7
4 CURVATURE EQUATIONS authKW 247444 1% 100% 5
5 AFFINE AREA authKW 197955 1% 100% 4
6 KAHLER RICCI FLAT authKW 197955 1% 100% 4
7 MULTI VALUED SOLUTIONS authKW 197951 1% 67% 6
8 PARABOLIC MONGE AMPERE EQUATION authKW 161656 1% 47% 7
9 HESSIAN OPERATORS authKW 158363 1% 80% 4
10 HESSIAN EQUATIONS authKW 151552 1% 44% 7

Web of Science journal categories


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 Mathematics 27937 90% 0% 558
2 Mathematics, Applied 7196 43% 0% 265
3 Multidisciplinary Sciences 3 1% 0% 4
4 Physics, Particles & Fields 0 1% 0% 8
5 Physics, Mathematical -0 1% 0% 4
6 Mechanics -0 1% 0% 6
7 Computer Science, Software Engineering -0 0% 0% 2
8 Operations Research & Management Science -1 0% 0% 1
9 Astronomy & Astrophysics -2 1% 0% 5
10 Computer Science, Interdisciplinary Applications -3 0% 0% 1

Address terms


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 CHALMERS UNIV TECHNOL MATH 49489 0% 100% 1
2 CNRS MATH UMR6085 49489 0% 100% 1
3 MATEMAT ESI INFORMAT 49489 0% 100% 1
4 PROJECT PN II ID PCE 2012 4 0021 39589 0% 40% 2
5 ANAL MATH SYST INFORMAT 24743 0% 50% 1
6 MATH UFR 920 24743 0% 50% 1
7 NEW PROC GEAR 24743 0% 50% 1
8 UMPA 46 24743 0% 50% 1
9 MATH COMPLEX SYST 17492 3% 2% 16
10 UFR MATH 920 16495 0% 33% 1

Journals


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS 20963 4% 2% 26
2 RESULTS IN MATHEMATICS 15832 2% 2% 15
3 COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS 14965 4% 1% 22
4 COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 12748 4% 1% 25
5 ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE 9031 2% 1% 15
6 JOURNAL OF DIFFERENTIAL GEOMETRY 7390 3% 1% 16
7 MATHEMATISCHE ZEITSCHRIFT 5625 4% 0% 24
8 CHINESE ANNALS OF MATHEMATICS SERIES B 4970 2% 1% 13
9 INDIANA UNIVERSITY MATHEMATICS JOURNAL 4657 2% 1% 15
10 JOURNAL OF DIFFERENTIAL EQUATIONS 3927 4% 0% 24

Author Key Words


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class		 LCSH search Wikipedia search
1 MONGE AMPERE EQUATION 507711 8% 21% 49 Search MONGE+AMPERE+EQUATION Search MONGE+AMPERE+EQUATION
2 HESSIAN EQUATION 375064 2% 63% 12 Search HESSIAN+EQUATION Search HESSIAN+EQUATION
3 BERNSTEIN PROPERTY 346422 1% 100% 7 Search BERNSTEIN+PROPERTY Search BERNSTEIN+PROPERTY
4 CURVATURE EQUATIONS 247444 1% 100% 5 Search CURVATURE+EQUATIONS Search CURVATURE+EQUATIONS
5 AFFINE AREA 197955 1% 100% 4 Search AFFINE+AREA Search AFFINE+AREA
6 KAHLER RICCI FLAT 197955 1% 100% 4 Search KAHLER+RICCI+FLAT Search KAHLER+RICCI+FLAT
7 MULTI VALUED SOLUTIONS 197951 1% 67% 6 Search MULTI+VALUED+SOLUTIONS Search MULTI+VALUED+SOLUTIONS
8 PARABOLIC MONGE AMPERE EQUATION 161656 1% 47% 7 Search PARABOLIC+MONGE+AMPERE+EQUATION Search PARABOLIC+MONGE+AMPERE+EQUATION
9 HESSIAN OPERATORS 158363 1% 80% 4 Search HESSIAN+OPERATORS Search HESSIAN+OPERATORS
10 HESSIAN EQUATIONS 151552 1% 44% 7 Search HESSIAN+EQUATIONS Search HESSIAN+EQUATIONS

Core articles
The table includes core articles in the class. The following variables is taken into account for the relevance score of an article in a cluster c:
(1) Number of references referring to publications in the class.
(2) Share of total number of active references referring to publications in the class.
(3) Age of the article. New articles get higher score than old articles.
(4) Citation rate, normalized to year.


Rank Reference # ref.
in cl.		 Shr. of ref. in
cl.		 Citations
1 GUAN, B , (2014) SECOND-ORDER ESTIMATES AND REGULARITY FOR FULLY NONLINEAR ELLIPTIC EQUATIONS ON RIEMANNIAN MANIFOLDS.DUKE MATHEMATICAL JOURNAL. VOL. 163. ISSUE 8. P. 1491 -1524 25 89% 7
2 WANG, XJ , (2009) THE K-HESSIAN EQUATION.GEOMETRIC ANALYSIS AND PDES. VOL. 1977. ISSUE . P. 177-252 25 76% 33
3 TIAN, BP , FU, YQ , (2014) EXISTENCE OF VISCOSITY SOLUTIONS FOR HESSIAN EQUATIONS IN EXTERIOR DOMAINS.FRONTIERS OF MATHEMATICS IN CHINA. VOL. 9. ISSUE 1. P. 201-211 20 91% 0
4 NAKAMORI, S , TAKIMOTO, K , (2015) A BERNSTEIN TYPE THEOREM FOR PARABOLIC K-HESSIAN EQUATIONS.NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS. VOL. 117. ISSUE . P. 211 -220 15 100% 1
5 JIAO, HM , (2016) C-1,C-1 REGULARITY FOR AN OBSTACLE PROBLEM OF HESSIAN EQUATIONS ON RIEMANNIAN MANIFOLDS.PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. VOL. 144. ISSUE 8. P. 3441 -3453 14 93% 1
6 TIAN, GJ , WANG, XJ , (2010) MOSER-TRUDINGER TYPE INEQUALITIES FOR THE HESSIAN EQUATION.JOURNAL OF FUNCTIONAL ANALYSIS. VOL. 259. ISSUE 8. P. 1974-2002 16 94% 8
7 WANG, C , BAO, JG , (2013) NECESSARY AND SUFFICIENT CONDITIONS ON EXISTENCE AND CONVEXITY OF SOLUTIONS FOR DIRICHLET PROBLEMS OF HESSIAN EQUATIONS ON EXTERIOR DOMAINS.PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. VOL. 141. ISSUE 4. P. 1289-1296 14 100% 1
8 HONG, JX , HUANG, GG , WANG, WY , (2011) EXISTENCE OF GLOBAL SMOOTH SOLUTIONS TO DIRICHLET PROBLEM FOR DEGENERATE ELLIPTIC MONGE-AMPERE EQUATIONS.COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. VOL. 36. ISSUE 4. P. 635-656 15 94% 7
9 LIN, TY , (2016) ON THE LOCAL ISOMETRIC EMBEDDING IN (3) OF SURFACES WITH ZERO SETS OF GAUSSIAN CURVATURE FORMING CUSP DOMAINS.COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. VOL. 41. ISSUE 10. P. 1553 -1592 15 83% 0
10 XU, RW , CAO, LF , (2014) BERNSTEIN PROPERTIES FOR ALPHA-COMPLETE HYPERSURFACES.JOURNAL OF INEQUALITIES AND APPLICATIONS. VOL. . ISSUE . P. - 13 100% 0

Classes with closest relation at Level 1


Rank Class id link
1 24886 AFFINE DIFFERENTIAL GEOMETRY//AFFINE HYPERSPHERES//AFFINE SPHERE
2 14786 PLURISUBHARMONIC FUNCTION//COMPLEX MONGE AMPERE OPERATOR//PLURICOMPLEX GREEN FUNCTION
3 8449 OPTIMAL TRANSPORT//OPTIMAL TRANSPORTATION//MONGE KANTOROVICH PROBLEM
4 13801 INFINITY LAPLACIAN//VISCOSITY SOLUTIONS//FULLY NONLINEAR EQUATIONS
5 7899 MEAN CURVATURE FLOW//CURVATURE FLOW//SELF SHRINKER
6 15989 BERNOULLI PROBLEM//FREE BOUNDARY PROBLEM//FREE BOUNDARY
7 9153 KAHLER METRICS//KAHLER EINSTEIN METRIC//BALANCED METRICS
8 1791 CONSTANT MEAN CURVATURE//SPACELIKE HYPERSURFACE//GEOMETRIA TOPOL
9 7600 Q CURVATURE//CRITICAL POINTS AT INFINITY//YAMABE PROBLEM
10 11417 LARGE SOLUTIONS//BOUNDARY BLOW UP//KARAMATA REGULAR VARIATION THEORY

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