For all nonsingular projective $n$-folds $V$ of general type, we prove the existence of Noether type inequalities in the following form:

$$\text{vol}(V)\geq a_{n,k}h^0(\Omega_V^k)-b_{n,k}$$

where $0< k\leq n$, $a_{n,k}$ and $b_{n,k}$ are positive constants only depending on $n$ and $k$. As applications, we determine the minimal volume for $3$-folds of general type with $\chi(\mathcal{O})\neq 2,3$ and disclose a new type of lifting principles for the sequence of canonical stability indices for varieties of general type. Finally we prove a theorem about “strong lifting principle” on varieties $X$ of general type with $q>\dim(X)$.This is based on a joint work with Zhi Jiang.