The study of degenerate Monge-Ampère equations
Research gap analysis derived from 3 mathematics papers in our local library.
The gap
The study of degenerate Monge-Ampère equations on non-compact complex manifolds. The application of the results of the paper to other areas of mathematics and physics.
Evidence profile
Sourced from the future-work section and stated research gap of the source papers, classified as general, spanning 3 journals.
Research trend
Established — well-defined area with open sub-problems.
Supporting evidence — 4 representative gaps
- Monge-Ampère equations with prescribed singularities on compact Hermitian manifolds (2026) · Journal of Functional Analysis · doi
The study of degenerate Monge-Ampère equations on non-compact complex manifolds. The application of the results of the paper to other areas of mathematics and physics.
generalfuture-work sectionevidence 5/5Keywords: study degenerate monge-amp equations non-compact complex manifolds application - On some connections between Kobayashi geometry and pluripotential theory (2026) · Transactions of the American Mathematical Society · doi
The paper identifies a gap in understanding the relationships between Kobayashi geometry and the Dirichlet problem for the complex Monge-Ampère equation. The authors highlight the need for further research in this area and provide a direction for future studies.
generalstated research gapevidence 5/5Keywords: paper identifies gap understanding relationships between kobayashi geometry - On some connections between Kobayashi geometry and pluripotential theory (2026) · Transactions of the American Mathematical Society · doi
The paper suggests future research directions, including the further study of connections between Kobayashi geometry and the Dirichlet problem for the complex Monge-Ampère equation. The authors propose exploring the properties of domains with nice boundary geometry and their relationship to the complex Monge-Ampère equation.
generalfuture-work sectionevidence 5/5Keywords: paper suggests future research directions including further study - The Dirichlet Problem for Monge-Ampère Type Equations on Riemannian Manifolds (2026) · Results in Mathematics · doi
The Dirichlet problem for Monge-Ampère type equations on Riemannian manifolds was not previously studied. Prior work only considered the Monge-Ampère equation in Euclidean space.
generalstated research gapevidence 5/5Keywords: dirichlet problem monge-amp type equations riemannian manifolds was
Questions about this gap
Explore this gap further
Run this gap as a query across open scholarly engines for the latest related literature.
Working on this gap? Review it with us.
Science AI Journal reviews manuscripts in one pass with 8 specialised AI agents calibrated on 69,000+ real peer reviews.
Tools for your next paper
Related gaps in Mathematics
- The paper identifies a gap in the literatureThe paper identifies a gap in the literature, specifically the need for a system that captures logic's most basic concepts, such as consiste…
- The study of the behavior of the p-Laplace equationThe study of the behavior of the p-Laplace equation on more general domains. The application of the paper's results to other optimization pr…
- Fractional partial differential equations do not acquireFractional partial differential equations do not acquire exact solutions in closed form. There is a need for numerical methods to solve such…
- The application of the proposed method to other complexThe application of the proposed method to other complex systems. The development of new numerical schemes for solving fractional differentia…