Pogorelov type interior C² estimate for Hessian quotient equation and its application

Key Points

• The study establishes a Pogorelov type interior C2 estimate for the Hessian quotient equation, enhancing understanding of geometric measures.
• When considering convex viscosity solutions, it shows that solutions are regular for k ≤ n-3 under certain conditions, advancing the field.
• This work compares different conditions for regularity using C1,α and W2,p spaces, indicating sharpness in the conditions set.
• The findings contribute to the theory of partial differential equations, potentially impacting further research in geometric analysis.